In this paper we present computer simulations of interstellar cloud collisions that for a given range of initial conditions could favor stellar cluster formation. We first construct a single spherical molecular hydrogen cloud with the Plummer radial density distribution with rigid rotation and an m = 2 density perturbation. The isolated cloud collapses into a filament with no sign of fragmentation. We then place two clouds for a head-on collision, and for an oblique collision characterized by an impact parameter that depends on the initial radius of the cloud. The approaching velocity of the clouds is changed from zero up to thirty times the gas sound speed. We have found that for certain values of our parameter space fragmentation into a stellar cluster is possible.