In this work, an extension of the magnetic field and force model for two cylindrical permanent magnets is introduced. The magnetic field model is established by using the magnetic charge method. Based on the model of the previously published work, an extension model is proposed. The magnetic interaction force model is built for a more general case where the axes of two cylindrical magnets are crossed. The simulations were performed via both the semi-analytical method using MATLAB® and the finite element analysis (FEA) method via a simulation software. The simulation results of the semi-analytical method and FEA have excellent agreement for all investigating cases of magnetic field and force, which depend on geometry parameters and the relative positions of the two magnets. The highest average modeling error is only 1.15%. For the specific cases, the simulation results also match very well with the results of other published works.