The overhead electrification system for high speed trains is modeled by a three degree of freedom pantograph and an infinite homogeneous and elastically supported beam. Travelling wave solutions for the beam with a moving load are used to derive an equivalent stiffness for the pantograph model. The model is new in that it takes account of transverse motion due to catenary zig-zag effects. Finite element solutions are also obtained for the moving load problem. The results show that transverse zig-zag effects are the primary expected motion in this system. The calculations also show the expected importance of critical wave speeds in these systems