The paper investigates the phenomenon of sand production in both axial and radial flow conditions using a coupled particle erosion-fluid transport-stress model that has been developed recently by the authors. We first examine sand production and wormhole growth in a sand pack as heavy oil is being drawn from it through a small orifice. Numerical results are in close agreement with experimental data available for the sand pack experiment. In particular, the computed porosity field and its temporal evolution during wormhole propagation match very well with available CT scan images of the sand pack. Then, we model a sand production hollow cylinder test in which sand is being produced under combined axial and radial flow of light oil in a sandstone specimen. Aspects such as sand flux and porosity evolutions, as well as erosion growth around the inner wall of the cylinder are investigated using the numerical model.