Prior experiments on shape constancy from novel views are inconclusive: Some show that shapes of objects can be recognized reliably from novel views, whereas others show just the opposite. Our analysis of prior results suggests that shape constancy from novel views is reliable when the object has properties that constrain its shape: The object has volumetric primitives, it has surfaces, it is symmetrical, it is composed of geons, its contours are planar, and its images provide useful topological information about its three-dimensional structure. To test the role of some of these constraints, we performed a set of experiments. Solid shapes (polyhedra) were shown on a computer monitor by means of kinetic depth effect. Experiment 1 showed that shape constancy can be reliably achieved when a polyhedron is represented by its contours (most of the constraints are present), but not when it is represented by vertices or by a polygonal line connecting the vertices in a random order (all the constraints are absent). Experiments 2 and 3 tested the role of individual constraints. Results of these experiments show that shape constancy from novel views is reliable when the object has planar contours and when the shapes of the contours together with topological information about the relations among the contours constrain the possible interpretations of the shape. Symmetry of the object and the topological stability of its image also contribute to shape constancy.