In this paper a new type of hybrid reluctance actuator is presented. This linear hybrid reluctance actuator is a two phase double sided actuator in which the stator is composed by four normalized U cores, each with a coil wrapped around the yoke connecting the two arms of the core or with two coils wound on each of the arms and a permanent magnet placed near the air gap between and in contact with both arms. The mover is comprised of rectangular poles without connecting iron pieces between them but mechanically joined by non-magnetic mounting parts. The magnets are arranged so that their flux is in parallel to the flux created when the coils are energized, both fluxes are added and the total reinforced flux links the stator and the mover. But when no currents flow through the coils no flux crosses the air gap, and the flux of the magnets is closed through the back iron that supports them. An analysis and simulation of the motor using 2 D finite element and MATLAB Simulink is carried out. Finally, a comparison of this type of actuator with respect a linear reluctance stepper motor of the same size is shown.