The electric and magnetic properties of high temperature superconductors and the possibility to cool them by cheap liquid nitrogen makes them attractive in power applications. An all superconducting linear synchronous motor is presented in this paper in order to quantify the benefits and disadvantages of such applications. The term ?all superconducting? is related with the absence of copper conductors and iron parts. Certain characteristics of the superconducting materials impose severe restrictions when used, e.g., as armature windings. A numerical method for deriving the thrust and lift forces developed in such a motor, driven by a typical current inverter, is presented.