[en] We develop a tool for numerical construction of femtosecond laser pulse propagation in air. The model is based on 2D+1 nonlinear Schroedinger equation (NLSE). Several nonlinear physics effects are considered in this full model which includes High-order Kerr effect (HOKE), Raman Kerr contribution, plasma absorption and defocusing. It is often implemented in laboratory with weak focusing optics for better observation, and the practical applications always involve collimated or nearly collimated beams. Here, we carry out a series of simulation on propagation of collimated femtosecond laser pulse in air, with peak power around the critical power for self-focusing (P_cr). The results are shown for peak power respectively equal to 0.3 and 1.9 P_cr. Especially, we numerically construct a complex physical processes image involving filamentation which is regarded as a delicate task to interpret numerical results with many competing effects. The results show a dynamic equilibrium between Kerr self-focusing and HOKE in case of 1.9P_cr. HOKE shows dominant in the competition of nonlinear effects so as to balance Kerr self-focusing, at least for the pulse with 100 fs at 800 nm. Our analysis is in accordance with the Marburger's prediction and image found in published literatures. Perspective of these works will be dedicated to describe the propagation of ultrashort pulses (around 15 fs) with NA ∼ 0.1 in the context of laser ablation in order to shed light on the significance of air on the outcomes of the laser-matter interaction. (author)