Symmetry is usually computationally expensive to encode reliably, and yet it is relatively effortless to perceive. Here, we extend F. J. A. M. Poirier and H. R. Wilson's (2006) model for shape perception to account for H. R. Wilson and F. Wilkinson's (2002) data on shape symmetry. Because the model already accounts for shape perception, only minimal neural circuitry is required to enable it to encode shape symmetry as well. The model is composed of three main parts: (1) recovery of object position using large-scale non-Fourier V4-like concentric units that respond at the center of concentric contour segments across orientations, (2) around that recovered object center, curvature mechanisms combine multiplicatively the responses of oriented filters to encode object-centric local shape information, with a preference for convexities, and (3) object-centric symmetry mechanisms. Model and human performances are comparable for symmetry perception of shapes. Moreover, with some improvement of edge recovery, the model can encode symmetry axes in natural images such as faces.