The disclosure relates to forming shaped thermoplastic articles having smooth edges. Many thermoplastic articles have sharp edges formed upon molding or cutting the article from a feedstock sheet. Such sharp edges can damage thin plastic films or flesh which they contact, and smoothing the edges is desirable. Described herein are methods of forming a smooth periphery for such sharp-edged articles by rolling over the sharp edge. The smoothing operation is performed by forming a deflectable flange including a bend region near the peripheral sharp edge, deflecting a portion of the deflectable flange by inserting it into the cavity of a frame-like upper body, optionally further deflecting the portion by inserting a ram into the cavity, and then heating and cooling the bend region to yield a smooth periphery. Alternatively, the smooth periphery can be formed by application of pressure sufficient to cause irreversible bending, with or without application of heat.