In the illusion, an assistant (Houdini employed his wife Bess) is locked inside a large box or trunk, often after being restrained with handcuffs, ropes, bags, etc. The magician stands upon the trunk and holds a curtain up to momentarily conceal his entire body. When the curtain is lowered, it is revealed to now be the assistant standing atop the box, the magician and assistant having changed places instantaneously. When the box is opened, it is shown to contain the magician, restrained as the assistant had been. In some acts, the magician is locked in the box first, then appears standing atop the box.
The Metamorphosis uses a device known as the substitution trunk, which has a secret panel that allows its occupant to sneak out. Having extricated himself from the sack in which he was tied, Houdini would climb out of the hidden door and crouch behind a curtain lifted by his wife. The two would quickly change places, Houdini appearing behind the curtain as Bess disappeared into the box. Bess would then emerge from the box and sack wearing a different costume.
In a variation on this method which is slightly more easily performed, the sack is in fact an open tube of hessian attached at one end around a hole in the back panel of the trunk. The magician steps into the tube (which appears to be a normal sack sitting inside the open trunk), and the sack is chained or otherwise sealed. By this point, the magician has slid out the tube and is hiding behind the rear of the trunk. The trick proceeds as normal from this point, with the assistant entering the trunk via the back rather than the hidden hatch.
Variations include the Aquarian Illusion performed by Mark Wilson, wherein a tank filled with water is used and a beautiful swimsuit-clad woman assistant is locked inside underwater, and Penn and Teller performing the illusion in an underwater theater with the female assistant handcuffed & locked in a steel cage on the bottom.
A method for Metamorphosis was exposed by the Masked Magician, Val Valentino, as part of Fox TV series Breaking the Magicians' Code: Magic's Biggest Secrets Finally Revealed. He was assisted by Michelle Berube. However, the method exposed (specifically the manner in which the trunk is opened) is not generally in use today.