In this paper, a mathematical model describing the deviation of the medical steel needle when it moves in the phantom of soft tissues (human tissues). This model will expect for use in the operational mode, where high precision positioning of the tip of the needle is necessary. The needle have asymmetric tip and because when the needle moves, it to deviate from rectilinear motion. Thus, by inserting and rotating the needle around its axis, it is possible to move the tip of the needle along a predetermined path. Consequently, having developed the model with its help, it will be possible to track the movement of the needle in the tissues or to predict optimal puncture points. The general formulation of the problems is considered and one of the sub-tasks is solved, as well as the available calculation of the needle tip deflection during the translational movement in a homogeneous material. The article shows the model used and the simulation results for different material densities and different needle tip angles. Comparison of the experimental data with the results obtained in the calculation using the proposed model is given.