We introduce a novel implicit representation for 2D and 3D shapes based on Support Vector Machine (SVM) theory. Each shape is represented by an analytic decision function obtained by training SVM, with a Radial Basis Function (RBF) kernel so that the interior shape points are given higher values. This empowers support vector shape (SVS) with multifold advantages. First, the representation uses a sparse subset of feature points determined by the support vectors, which significantly improves the discriminative power against noise, fragmentation, and other artifacts that often come with the data. Second, the use of the RBF kernel provides scale, rotation, and translation invariant features, and allows any shape to be represented accurately regardless of its complexity. Finally, the decision function can be used to select reliable feature points. These features are described using gradients computed from highly consistent decision functions instead from conventional edges. Our experiments demonstrate promising results.