In this book,I propose a Finite Element Methods analyzing applied to the linear tubular stepping actuator.The design requires the choice of appropriate tooth geometry.A study in open loop control using the software Matlab and Simulink is given to present the dynamic behavior,the currents and the control form.In closed loop control,I present S.M.C to eliminate the disturbance of the current when the motor load is important.Then to optimize the mechanical structure,my aim is to maximize the trust force taking into account the actuator's weight which is considering as the most important constraint.The contribution of the machine weight minimization is principally a cost decrease that permits its integration in small systems.The optimization method approach is evolutionary strategy method.F.E.A is then employed to calculate a series of designs and determine the optimum one.Then,I present the right choice between 2D and 3D mesh so that the F.E.A gets efficient solutions.After, I increase the solution accuracy by increasing the model's polynomial order while keeping constant the number of mesh elements in order to minimize the discretization error. THANKS TO INFOLYTICA CORPORATION