Flows of granular material on non-frozen and frozen heaps are considered numerically and theoretically in this work. The surface flow on a non-frozen heap is first investigated numerically using the discrete element method. The flow profiles of the surface granular flow and the creep motion of particles in the heap are studied. It is shown that the mean velocity of the surface flow exhibits a linear relationship with the distance from the heap surface, while that of the particles in the heap decays exponentially with the distance. The existence of such a creep motion may be attributed to the variation of the porosity distribution of the heap. The granular flow on a frozen static heap is also simulated, and compared with the one on the corresponding non-frozen heap. The results show that the surface conditions of the heap, to some extent, affect the flow upon it. The surface flow on a static heap is then theoretically examined in detail by using a recently developed continuum model. The depth of the steady-state surface flow and its dependence on wall friction and heap width are investigated. In addition, the theoretical results are compared with the DEM simulation results and the experimental ones in the literature, and qualitatively good agreements are observed.