This thesis describes the design, analysis and optimization of a linear motor for use in reciprocating electro-mechanical systems. A review of various types of limited range linear motion motors was undertaken and the most suitable design identified was that of the permanent magnet linear reluctance motor. These machines are rapidly replacing conventional electrical, mechanical and hydraulic systems in a wide range of applications, such as Stirling cycle cryogenic coolers, artificial heart devices and aircraft flight surface actuators. They take the form of a bi-directional moving-iron or variable air-gap device in which a soft-iron armature, positioned on the central axis of two opposing ring magnets, moves when a current is fed through a solenoidal coil situated between the magnets. An optimum design should possess a linear coil current/armature displacement characteristic, produce the maximum possible force on the armature and have a fast dynamic response. An essential requirement is a restoring axial stiffness, to ensure that the armature returns to its central position in the absence of any coil current. Due to the complex geometry of the device, and the non-linear magnetic materials involved, a finite element approach was used in studying the internal magnetic conditions. Following this, various dimensional changes were made to the magnetic circuit of the typical motor investigated, and different magnetic materials were employed to improve the static characteristics. A mathematical model that includes the drive system has been developed, employing tensor techniques, to accurately predict the dynamic performance. A factorial design approach has been used to identify the dimensions of the motor most significant in affecting the device performance, and an optimum design has been identified. Simulated and finite element results are compared with the experimental performance of various prototype motors, to illustrate the effectiveness of the modelling technique.