Abstract. Horizontal forces between the crane and the crane runway girder occur during a motion of an overhead travelling crane on the crane runway. There are several methods for calculation of these forces. The most significant load caused by motion of crane is the skewing and the acceleration of the crane and of the crab. This paper deals with the acceleration of the crane and with the skewing of the crane. In present the skewing of crane is defined as the motion of the overhead bridge crane with the constant velocity but with the angle relative to the crane runway. The transverse forces caused by acceleration of the crane are calculated separately. But the skewing of the crane can occur also during the accelerating of the crane. Present standards don’t take this situation into account. A dynamical model presented in this paper describes motion of the overhead double bridge crane during its acceleration. The basic assumption of this model is that there the contact between the rim of the firs crane wheel and the rail of the crane runway.