This study describes a mathematical model of deflection of a steel medical injection needle during its motion in the soft tissue phantom (imitation of human tissues). This model is necessary for adjustment of robotically assisted systems during brachytherapy procedures or similar operations where high precision needle tip positioning is prerequisite. Since the needle tip is asymmetrical, the needle will deform when moving in human tissues and consequently deflect from the rectirectilinear motion. Thus, by inserting and rotating the needle around its axis the needle tip can be led along the predetermined path. This study adopts a new approach to describe an external impact on the needle when it moves inside human tissues and also describes 2D and 3D models, a process of selection of coefficients for 3D models, and provides simulation results.