The introduction of Video Objects (VOs) is one of the innovations of MPEG-4. The α-plane of a VO defines its shape at a given instance in time and hence determines the boundary of its texture. In packet-based networks, shape, motion, and texture are subject to loss. In this paper we propose a post-processing shape error concealment technique that uses the motion compensated boundary information of the previously received α-plane. The proposed approach is based on matching received boundary segments in the current frame to the boundary in the previous frame. This matching is achieved by finding a maximally smooth motion vector field. After the current boundary segments are matched to the previous boundary, the missing boundary pieces are reconstructed by motion compensation. Experimental results demonstrating the performance of the proposed motion compensated shape error concealment method, and comparisons with our previously proposed spatial Hermite spline method are presented.