A system under gravity, made up of hard spheres with an internal degree of freedom, is studied on a 3d lattice under a Monte Carlo “tap” dynamics. A “jamming” transition similar to that found in real experiment is found. To understand the nature of such transition a simplified version of the model is also studied in a mean field approximation, using the statistical mechanics approach à la Edwards. A phase transition from a “fluid” to a “glassy” phase is found when crystallization is avoided. Interestingly, the nature of such a “glassy” phase turns out to be the same found in mean field models for glass formers.