A computer program has been developed to simulate the filtration process in fibrous filters collecting monodisperse aerosol particles. The model filter is represented by an array of parallel cylindrical fibers and the Kuwabara flow field is employed to determine the particles trajectories inside the filter. The simulation model is based on the Monte-Carlo (self-driven) principle, and a sequence of uniform pairs of pseudorandom numbers is generated representing the initial locations of the approaching particles. The estimation of the initial collection efficiency through the simulation model that considers the deposited particles and the presence of dendrites is in good agreement with published experimental data. The development of the quasi three-dimensional simulation model offers a detailed information about the transient progression of the deposition process. The transient behavior of the pressure drop across the collector system (the fiber and the collected particles) and the morphology of deposit are presented and the results are in good agreement with experimental data.