In this section we present a model of velocity vectors on a regular lattice [11,14]: the vectors evolve by means of binary inelastic collisions. This model seems to reproduce the phenomenology of a granular gas in the homogeneous phase and, more remarkably, in the first correlated phase, that is when velocity correlations grow up (development of the shear instability). The further density instability (clustering) is prevented by the homogeneity of the density which is imposed in our model. Molecular dynamics simulations of inelastic hard objects are very demanding on space and time scales needed to observe the shear instability and usually are not satisfactory in terms of duration and statistics, so that information on structure factors, p.d.f. of physical quantities and energy decay are usually lacking. This lattice model is a formidable alternative to address all these problems.