This paper discusses (semi-) analytical modeling techniques which are applied in the analysis and design of highprecision actuators which contain large multi-dimensional magnet arrays. Such high-precision actuators are being designed for application in the lithographic industry. The methods presented in this paper offer not only a significant reduction of the calculation time compared to three-dimensional finite element simulations, but also allow the calculation of force distributions inside the permanent magnet structures. The application of these models for the design of magnetically levitated planar actuators and for gravity compensation is discussed in detail.