Recent experiments on optical damage by ultrashort laser pulses have demonstrated that the temporal pulse shape can dramatically influence plasma generation in fused silica. We use a modified 3+1D nonlinear Schrödinger equation for the pulse propagation coupled to a rate equation for the plasma density in the dielectric material to simulate pulse propagation and plasma formation in fused silica. We use these simulations to analyze the influence of pulse shape and beam geometry on the formation of the electron plasma and hence modification in the bulk material. In particular, we simulate the effect of pulses reconstructed from experimental data. It is expected that a better understanding of the dynamics of laser-induced plasma generation will enable the accurate simulation of optical damage in a variety of dielectrics, ultimately leading to an enhanced control of optical damage to real materials and optical devices.