The disclosure relates to forming shaped thermoplastic articles having smooth peripheries. 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 separated from the potentially sharp peripheral edge by a spacer, deflecting a portion of the deflectable flange, and softening at least one bent portion of the deflectable flange to yield a smooth periphery upon cooling.