We present a model introducing the Landau–Lifshitz–Gilbert equation with a Slonczewski's Spin-Transfer-Torque (STT) component in order to take into account spin polarized current influence on the magnetization dynamics, which was developed as an Object Oriented MicroMagnetic Framework extension. We implement the following computations: magnetoresistance of vertical channels is calculated from the local spin arrangement, local current density is used to calculate the in-plane and perpendicular STT components as well as the Oersted field, which is caused by the vertical current flow. The model allows for an analysis of all listed components separately, therefore, the contribution of each physical phenomenon in dynamic behavior of Magnetic Tunnel Junction (MTJ) magnetization is discussed. The simulated switching voltage is compared with the experimental data measured in MTJ nanopillars.