This paper presents new semi-analytical expressions to calculate the self-inductance and the electromagnetic force for a ferromagnetic cylinder of finite length placed inside a circular coil of rectangular cross section. The proposed analytical model is based on boundary value problems with Fourier analysis. Laplace's and Poisson's equations are solved in each region by using the separation of variables method. The boundary and continuity conditions between the different regions yield to the global solution. Moreover, the iron cylinder is assumed to be infinitely permeable. Magnetic field distribution, self-inductance and electromagnetic force obtained with the proposed analytical model are compared with those obtained from finite-element.