We describe a method to compute three-dimensional force equilibria in the Earth's magnetosphere. The method is embodied in a code called the MagnetoFriction code which solves a set of ideal magnetohydrodynamic (MHD) equations that are modified to include a frictional dissipation term in the momentum equation. The friction takes the form of a force which is directed against the fluid motion and is therefore an energy sink. This allows the system to settle into a minimum energy equilibrium. A nonuniform cartesian grid is used along with initial conditions supplied by empirical magnetic field and pressure models. These initial conditions do not, in general, satisfy the force balance condition $vec{J} times vec{B} = nabla_{p}$, and the code must iterate until approximate force balance is achieved. Pressure and magnetic field solutions are presented for several different configurations of the magnetosphere.