A simple and efficient method for the solution of open-boundary axisymmetric electric and magnetic field problems is presented. Firstly, the classical Kelvin transformation approach is reviewed. The proposed axisymmetric approach uses the conventional Kelvin transformation coupled with a calculation procedure to alter the value of the parameters that represent the material properties of the exterior region. This technique is analyzed computationally with a force calculation problem and two numerical models are employed. In the first model, the exterior problem is modeled using the axisymmetric Kelvin transformation approach, and the forces are calculated using the weighted Maxwell stress tensor method. In the second model, asymptotic boundary conditions are used to terminate the solution region, and the forces are calculated using the Lorentz formula. Numerical results produced by the two models show an excellent correlation.