Recently ultrashort laser pulses became most important for micro structuring and biomedical applications such as refractive surgery. Ultrashort laser pulses tightly focused to a small spot easily provide intensity sufficient to induce nonlinear ionization. A plasma is generated and heated in the focus resulting in optical breakdown. The energy deposited in the plasma and the mechanical effects subsequent to optical breakdown are utilized by modern applications of ultrashort laser pulses to induce controlled highly reproducible material alteration. A model including both nonlinear pulse propagation and plasma generation is introduced to numerically investigate the interaction of ultrashort laser pulses with the self-induced plasma in the vicinity of the focus. The numerical code is based on a (3+1)-dimensional nonlinear Schroedinger equation describing the pulse propagation. A multi rate equation model recently published by B. Rethfeld is used to simultaneously calculate the generation of free electrons. It is the first numerically simple approach to describe nonlinear ionization that allows a non static energy distribution of free electrons in the conduction band. The code is applicable to any transparent Kerr medium, whose linear and nonlinear optical parameters are known. Numerical calculations based on this model are used to understand the dependence between the size, the geometry and the free electron density of ultrashort laser pulse induced optical breakdown plasmas in various focusing geometries. The code enables to use arbitrary initial conditions for the laser field in the focus. More realistic focusing scenarios than the simple assumption of focused gaussian beams can be taken into account. Nonlinear side effects, such as streak formation occurring in addition to optical breakdown during ultrashort pulse refractive eye surgeries can be numerically investigated.