In classical hydrogeology land subsidence due to fluid withdrawal is typically predicted by decoupling the flow model from the structural model. The pore pressure solution obtained from the flow model is used as an external source of strength in the structural equations to compute the porous medium deformation. Though the horizontal displacement can be of some interest as well, usually the attention is devoted to the vertical displacement, which allows for the prediction of subsidence at the ground surface. A careful inspection of the equilibrium equations, together with a few assumptions related to the subsidence mechanism, leads to the development of a simplified model based on one anisotropic diffusion equation for the vertical displacement only. The model can be applied to a generally heterogeneous porous medium, possibly with a non linear or plastic mechanical behavior, and subject to an arbitrary pore pressure variation. The aim of the present paper is to investigate the conditions under which such a model provides results of comparable accuracy with respect to the solution of the classical equilibrium equations. A sensitivity analysis is performed on the Poisson ratio, which controls the model anisotropy, the depleted reservoir depth and shape, and the rock mechanical heterogeneity. The results show that the diffusion model of subsidence gives a good prediction especially in case of a thin depleted reservoir embedded within homogeneous or generally heterogeneous porous media with a Poisson ratio between 0.20 and 0.30, i.e. the vast majority of real applications. The above model allows also for a novel interpretation of the volumetric locking phenomenon occurring for a Poisson ratio close to 0.50 and helps gain a new insight in terms of equivalent "mechanical conductivities" into the propagation of the deep compaction to the land surface.