The macaque anterior intraparietal area (AIP) is crucial for visually guided grasping. AIP neurons respond during the visual presentation of real-world objects and encode the depth profile of disparity-defined curved surfaces. We investigated the neural representation of curved surfaces in AIP using a stimulus-reduction approach. The stimuli consisted of three-dimensional (3-D) shapes curved along the horizontal axis, the vertical axis, or both the horizontal and the vertical axes of the shape. The depth profile was defined solely by binocular disparity that varied along either the boundary or the surface of the shape or along both the boundary and the surface of the shape. The majority of AIP neurons were selective for curved boundaries along the horizontal or the vertical axis, and neural selectivity emerged at short latencies. Stimuli in which disparity varied only along the surface of the shape (with zero disparity on the boundaries) evoked selectivity in a smaller proportion of AIP neurons and at considerably longer latencies. AIP neurons were not selective for 3-D surfaces composed of anticorrelated disparities. Thus the neural selectivity for object depth profile in AIP is present when only the boundary is curved in depth, but not for disparity in anticorrelated stereograms.