The article presents the analytical model of a linear/rotary solid-state actuator formed by a shape memory wire wound over a cylindrical drum. The model assumes a bilinear w temperature) and a linear elastic response in the austenitic state (high temperature). Based on simple equilibrium conditions, the model calculates the stress and strain distributions in the wire when subjected to a constant external backup force and undergoing frictional sliding forces at the contact with the drum. Closed-form expressions are supplied for the stroke produced by whatever actuator geometry and are validated numerically against finite element results. For a particular actuator configuration, the analytical forecasts are also checked experimentally on a proof-of-concept prototype. The analytical model shows that large strokes (up to one-half of the drum’s diameter) are achieved if the frictional coefficient is kept below 0.01. Rolling-contact architectures or sonic-pulse excitations of the drum are discussed as technical solutions to obtain such low friction values.