The mobile robots which can move on complicated working surfaces play a significant role in the automation of various technological processes, in particular, ship repair, fire fighting, inspection of welding quality, rescue operations, etc. This work is a continuation of the authors’ investigation of the mobile robot’s moving on inclined and vertical ferromagnetic surfaces based on a magnetically operated wheel-mover. Special attention is paid to constructing magnetically operated wheel-mover with twelve legs and modeling of the robot’s wheel-mover behavior in different working modes including investigations of the wheel-mover center trajectory, behavior of control signals, etc. Geometrical dependences between a number of wheel-mover legs and deviation of the wheel center path from horizontal line are described. In the present article the modeling results for movement of the wheel-mover on both plain and non-plain surfaces are discussed. For this purpose, the mathematical model of the wheel-mover was created and analyzed and the results were verified using a simulation approach.