Ultrashort laser pulses tightly focused provide intensity sufficient to initialize nonlinear ionization processes. Thus a plasma is generated in the focal region eventually resulting in optical breakdown. The deterministic character of this nonlinear interaction enables the generation of precise and highly reproducible material alteration. To gain better spatial precision applications have recently evolved strongly towards tight focusing of ultrashort pulses using microscope objectives as focusing units. The pulse energy required to generate optical breakdown was thus reduced to nanojoules or even below. The mechanical effects subsequent to plasma generation can be minimized to the very focus. Cell surgery with ultrashort pulses enables to precisely ablate cell organelles without observable hazardous effects to the surroundings or the entire cell. To numerically investigate the nonlinear interaction of ultrashort pulses with transparent media, a model including both nonlinear pulse propagation and plasma generation is introduced. The numerical code is based on a (3+1)-dimensional nonlinear Schrödinger equation describing the pulse propagation and the interaction with the density of free electrons that are generated in the focus. The nonlinear wave equation was derived taking into account both nonparaxial and vectorial effects to accurately include tight focusing at high numerical aperture. A multi rate equation model for dielectrics recently published by B. Rethfeld is used to simultaneously calculate the generation of free electrons. Numerical calculations based on this model are used to understand the dependence between size, geometry and density of optical breakdown plasmas in various focusing geometries of high numerical aperture. The code enables to use arbitrary initial conditions for the laser field in the focus. At high numerical aperture it is most important to start the simulation using realistic initial conditions. Especially the vectorial character of the electric field is most important to be considered. Thus a vectorial diffraction integral was used to calculate initial conditions at high numerical aperture. The code is applicable to any transparent Kerr medium, whose linear and nonlinear optical parameters are known. Within this work the code was applied to water as a model substance to biological soft tissue and cellular constituents.