Particles produced by the hydro-mechanical processes during sanding in hydrocarbon wells is a highly complex physical process. Sanding onset is influenced by a number of factors which include mechanical failure and hydrodynamic erosion. Over the years a number of mathematical and numerical models have been developed to describe the sand production process, involving sanding criteria or constitutive laws of mechanical or hydro-dynamical nature. In this work we propose a new simplified model working along the lines of the hydro-dynamical constitutive law of previous research works. The model amounts to a set of two ordinary differential equations coupling the mechanical process of plastic yielding with hydro-dynamic erosion, including degradation of the material. The model is constructed for hollow cylinder tests which allows cylindrical symmetry which is particularly useful for determining the sand production coefficient λ from such tests. The sand production coefficient as a function of the externally applied stress is estimated from previously published experimental data via a single parameter best fit. It is shown that the sand production coefficient is nearly constant for the range of values of the external stress considered. Additionally, the mathematical sand production curves capture fairly well the experimental data.