In this paper we focus on the case of sandstones for which many experimental data are available. We present a simple 2‒D model derived from granular media mechanics. This model assumes that the granular microstructure is a key point to understand the mechanical behavior. We consider a periodic grain network and focus on the first‒order neighbors of a given grain. These approximations are sufficient to explain the overall mechanical behavior in the Q versus P stress space. In the low pressure range, the controlling micromechanism is assumed to be tensile failure at grain contacts. The “dilatant” envelope is found to be a straight line in the stress space. In the high pressure range, the controlling micromechanism is assumed to be grain fragmentation. The “compactant” envelope is found to be a straight line in the stress space. We observed that this 2‒D model slightly overestimates Q versus P slopes determined experimentally (2.3 instead of 1.5), which can be explained by the approximations made.