Despite the remarkable complexity of our hands, we effortlessly use them to grasp and manipulate objects. To achieve dexterous object manipulation requires not only a sophisticated motor system to move the hand but also a sensory system to provide sensory feedback — proprioceptive and tactile — about the consequences of those movements. While some progress has been made to understand the neural basis of touch in somatosensory cortex, much less is known about the neural basis of hand proprioception. To fill this gap, we simultaneously record time-varying joint kinematics of the hand — measured using a camera-based motion tracking system — and neural activity from somatosensory and motor cortices of rhesus macaques — using chronically implanted electrode arrays — as they perform natural grasping movements and are subjected to passive hand movements. We find that somatosensory representations of kinematics are very similar to their motor counterparts, with spiking activity preferentially encoding the postures (not the velocities) of multiple joints spanning the entire hand. Preferential encoding of hand posture stands in stark contrast to models of kinematic encoding of the shoulder and elbow, where velocities are preferentially encoded. Moreover, we observe similar response properties in somatosensory and motor cortices during both active and passive movements of the wrist and digits. We conclude that hand shaping via movements of the digits and wrist relies on different neural mechanisms than does hand transport via movements of the arm.