A new form of a linear reluctance motor is described, comprising two flat rectangular plates of mild steel separated by a small airgap by means of linear bearings. One plate, which is fixed, acts as the stator, which accommodates a 3-phase distributed winding. Small square-cross-section slots are cut on the inside stator surface with a 2-start lead on similar slots cut orthogonally on the moving plate (the armature). Linear displacement is achieved by controlling the phase of the excitation supply in relation to the points of minimum reluctance. The motor is capable of operating over displacements of 1 m, or more, with good positional accuracy and a relatively low speed. The basic performance of the machine is described, and theoretical figures are compared with the experimental results obtained on a prototype motor.