Robert Louis Stevenson's short novel has been adapted for the RSC by David Edgar and directed by Peter Wood. Everyone knows how Dr Jekyll, the respectable Victorian gentleman, turns into Mr Hyde, the fiendish doer of unspeakable deeds. The schoolboy conception of the story is essentially the right one: a man in evening dress looks into the mirror and watches, aghast, as he turns into a hairy monster before slouching off into the, murky night.

Stevenson's book is a study in duality and takes its place alongside other 19th-century works on a similar theme by Dostoevsky and Oscar Wilde. It is also a literary response to Darwinism - at one point Dr Jekyll describes Hyde as 'the animal within me licking the chops of memory'. Less well known (except perhaps to Scottish schoolboys) is the peculiar Scottishness of Stevenson's tale. The strictures of Calvinism and life in bourgeois Edinburgh - from which the young Stevenson himself fled - form the background to Mr Hyde's light-headed sense of release when committing his blasphemous and bestial acts. There is, too, an autobiographical significance about the piece. Stevenson's relationship with his disapproving father was turbulent. Mr Hyde (who is very much younger than Dr Jekyll) expresses some of Stevenson's filial rebelliousness.

What turns all these elements into something darkly compelling is Stevenson's mastery of his narrative. The mystery unfolds through the investigations of Dr Jekyll's staid lawyer friend Mr Utterson (played with dry melancholy by Oliver Ford Davies), and it is only at the very end that the hauntingly unthinkable truth - Dr Jekyll and Mr Hyde are the same person - is brought home. The full history of Dr Jekyll's chemical and moral experiments are given in the form of a long statement, read posthumously, in which all the threads that so baffled the lawyer are tied together. In this way the element of suspense is sustained right up to the end.

This poses a problem for the dramatist. It is hard to see how a stage version could work that left this essential discovery until last. David Edgar rightly gives us the transformation in front of the mirror early on. But once Roger Allam's Dr Jekyll has swallowed the potion and seen Simon Russell Beale's dwarfish Mr Hyde materialise before him, what else can the dramatist do but give us a game of hide, and seek?

David Edgar decides to 'place' Dr Jekyll in both his social and his family history. Dr Jekyll acquires a sister, Katherine (Pippa Guard). Unlike her buttoned-up brother, Katherine is a proto-New Woman. Jekyll himself becomes more and more a routine psychological case of Freudian repression. His mortification of the flesh (he is unmarried) provokes lustful fantasies which he acts out with his sister's maid Annie (Katrina Levon). The roots of his problems are traced back to an unloved childhood, When, we gather, his sister was the apple of her father's eye. Jekyll savours the memory of severely bashing his little sister and this becomes the focal event for Hyde's subsequent amorality.

The exposition becomes more and more laboured. Katherine wears a symbolic eye patch - she suffers from double vision brought on by the childhood incident - and she keeps seeing two of her brother. Their father, we learn, was a 'fiend in human form'. Katherine gives Jekyll his old medical note books and it is from them that he carries on experiments started and abandoned by his late father. Katherine's little children play with a spinning top that has a smiling face painted on one side, a frowning face on the other. There is no danger of missing the point.

This heavy-handed insistence, is carried over into Edgar's treatment of Victorian social hypocrisy. All the male protagonists harbour guilty secrets - mainly to do with seducing young women and casting them out. Personal repression leads to social repression, you see. As if this had not been made clear, Jekyll encounters a country parson in the train who tells, with lubricious zeal, how young maids are shockingly seduced - adding, superfluously, 'Who can cast the first stone?' Jekyll meanwhile, in the course of the monologue, has metamorphosed into Hyde - this is one of the best creepy moments in the production.

But the production lacks dramatic charge. Apart from one or two moments when Jekyll threatens the safety of his sister's little children, there is little real menace. Worse, the moral debate between Jekyll and Hyde is conducted on a crushingly banal level. The two fine actors playing the parts try to inject urgency into it but flounder with lines like, 'How can we live without the good?'. I also doubt the wisdom of Edgar's introduction of facile jokiness into Hyde's speech.

Late in the second half the production starts to create an atmosphere of genuine tension. Jekyll is now turning into Hyde with greater frequency and unaided by any chemicals. Caught short, wanted for murder and without the potion to help him change back, Hyde persuades Jekyll's doctor friend to fetch it for him. Stumbling back to his rooms through the foggy gloom of night-time London, Jekyll collapses on to his couch, only to be awakened moments later by Hyde mockingly tapping the test tube with a spoon and saying in a bright breakfast DJ voice 'Bing bong'. It is like letting Kenny Everett wander into the final of Mastermind. However factitious the tension this is not the best way to sustain it. You can't help feeling that this production is a missed opportunity.

"No house without a cellar," wrote Kurt Tucholsky: if that is true of George, it should apply even more to the hero of The Strange Case of Dr Jekyll and Mr Hyde - except that in David Edgar's adaptation, the cellar has been displaced by the library. Not only does the subject of the Doppelgänger and its treatment in Goethe come .up among the doctor's dinner guests, together with projections of Stevenson's text on Carl Toms's revolving set; but Jekyll's main penalty after downing the fatal potion is to endure compulsory discussions with his disreputable opposite number. As each knows what is going through the other's head one wonders why they speak at all, much less maintain attitudes of high-toned outrage and Mephistophelian mockery.

The parts are extremely well played by Roger Allam (particularly when invaded by the spirit of Hyde) and Simon Russell Beale (particularly when polishing off a night-walking MP in Clockwork Orange style). But the brilliant physical transformations in Peter Wood's production are no substitute for having the story properly told. Mr Edgar also credits Jekyll with a sister whom he assaulted as a boy. You only learn this towards the end. Until then you are left feeling that poor Pippa Guard must really have hurt herself to be going through the show in a black eye patch.