This effect was made famous by Harry Houdini, an illusion he called Metamorphosis (means "change"). Also traditionally called a “Substitution trunk” (Sub Trunk for short), the magician displays a packing box style trunk. Volunteers from the audience can assist the magician by moving the trunk in place, opening the hinged lid, and giving the box a thorough inspection. Next the magician displays a pair of handcuffs or other wrist restraint device, and a large cloth bag.
The magician's assistant enters the trunk and then is handcuffed. Next she enters the bag and one of the volunteers tie the bag closed with a piece of rope. The assistant bends down inside the box, the lid is closed, and the trunk is locked. 

One of the real improvements in the Substitution Trunk effect occurred in the 1940's and 1950's with the addition of a canvas covering that fit around the trunk. Called the Canvas Covered Box, a canvas covering is placed around the trunk and is laced-shut in a fashion so that it is impossible for the lid to be opened.  

Next the magician hops-up on top of the trunk and raises a tubular curtain. On the simple count of three, the curtain is dropped, and the assistant is now standing on top of the trunk! The trunk is opened, and the magician is found in the trunk and handcuffed inside the cloth bag.
The Canvas Covered Box includes both the Sub Trunk – Deluxe and the canvas covering. Highly recommended, this addition tends to fool even magicians who are "in the know" regarding traditional sub trunk illusions. Note that the curtain, bag, and handcuffs are not supplied. These are additions that can be supplied for a reasonable price.