The collisional effect due to the multi-photon ionization process in dielectric material has been studied. We found that the breakdown threshold of fused silica is the same for both linearly and circularly polarized light at 55 fs and 100 fs, which we believe is an indication of the suppression of multi-photon ionization in solids. By numerically solving the time-dependent Schrodinger equation with scattering, for the first time, we have observed substantial reduction of the multi-photon ionization rate in dielectrics due to collisions.