This article is aimed at obtaining a description of the behaviour of an ideal differentially steered drive system (mobile robot) and planar motion. The mathematical dynamic model describing the motion (speed and direction) of one robot’s point is created based on the first principles approach. The trajectory of this point is converted to trajectories of wheel contact points with the plane of motion. The dynamic behavior of motors and chassis, form of coupling between motors and wheels and basic geometric dimensions are taken into account. The resulting trajectory depends on the supply voltage of both drive motors. The dynamic model will be used for design and verification of a robot’s motion control in MATLAB / SIMULINK simulation environment.