The wheel is a very important machine part. It is very often found in the construction of the vehicles. Therefore its dynamics must be studied properly. In the paper is presented the dynamical survey of a wheel which climbs on an inclined plane under the action of an active moment produced by an engine. The case of rolling without sliding was taken under consideration in the paper. The approach of the problem is a numerical one. The differential equations describing the movement of the motor wheel were written in matrix form. The paper also presents a method of removing of the constraint forces from the differential equations of motion.