This paper presents three types of magnetostatic models of ironless planar actuators with moving magnets. The models predict the force and torque exerted on the translator of the actuator, which can be positioned in six degrees-of-freedom with respect to the stator coils. The force and torque are calculated with the Lorentz force law. The analytical and numerical models can be used for the design of large planar actuators, for the fast comparison of actuator topologies, and in the decoupling and commutation algorithm. The models have been verified with experiments.