Singularity is an inherent property of robotic manipulators. A manipulator becomes singular when it gains or losses degrees of freedom at a particular configuration. In this work, a type of singularities caused by special shapes of platforms, either the mobile or the base platform, is addressed. This type of singularities pertains to the architecture singularity, but associated only with special shape designs of base and mobile platforms and spans in the whole workspace, which is referred as shape singularity. The paper provides formulations of shape singularity. The geometry and algebra properties of shape singularity are analyzed. Three examples of shape singularity identification for parallel mechanisms with prismatic joints are included, one for 3-DOF planar mechanisms, the others for 3-DOF and 6-DOF spatial mechanisms. The application of shape singularity in adjustable compliance mechanism design is illustrated.