A new parallel algorithm is proposed for detecting corners of multiple planar curves or shapes. This algorithm is based on an analysis of morphological residues and corner characteristics. The method is different from traditional chain-code based corner detection algorithms which associate with a chain coding and floating point computation. For multiple objects in an image, the proposed algorithm treats them uniformly and applies simultaneously on curves and shapes of multiple objects. The experiments demonstrate that the algorithm can be effectively executed on an SIMD parallel computer. A boundary-constrained morphological method is presented for filling closed curves into shapes which are subsequently used for corner detection.