Purpose The purpose of this study is to develop a magnetic resonance imaging (MRI)-safe iron-free electrical actuator for MR-guided surgical interventions. Design/methodology/approach The paper deals with the design of an MRI compatible electrical actuator. Three-dimensional electromagnetic and thermal analytical models have been developed to design the actuator. These models have been validated through 3D finite element (FE) computations. The analytical models have been inserted in an optimization procedure that uses genetic algorithms to find the optimal parameters of the actuator. Findings The analytical models are very fast and precise compared to the FE models. The computation time is 0.1 s for the electromagnetic analytical model and 3 min for the FE one. The optimized actuator does not perturb imaging sequence even if supplied with a current 10 times higher than its rated one. Indeed, the actuator’s magnetic field generated in the imaging area does not exceed 1 ppm of the B 0 field generated by the MRI scanner. The actuator can perform up to 25 biopsy cycles without any risk to the actuator or the patient since he maximum temperature rise of the actuator is about 20°C. The actuator is compact and lightweight compared to its pneumatic counterpart. Originality/value The MRI compatible actuator uses the B 0 field generated by scanner as inductor. The design procedure uses magneto-thermal coupled models that can be adapted to the design of a variety actuation systems working in MRI environment.