Grain piles embody the complex mechanics and kinematics of disordered granular materials, including solid-like and fluid-like behaviours, complex kinematics, and preparation history-dependent stress variation. It is widely believed that the bulk of a growing pile is static and flow is confined to a thin layer at the surface, but very few studies have investigated the subsurface kinematics. Here we study the flow within conical grain piles by flow imaging experiments and particle dynamics simulations. We provide direct evidence of continuous plastic flow deep within piles as grains are poured from above, and show that the direction of flow varies smoothly from vertical at the symmetry axis to parallel to the surface at the periphery. Our findings provide new insight into the kinematics and rheology of granular media, including the nature of creep in seemingly solid-like regions, and have important implications for geophysical phenomena such as landslides and industrial processes.