The characteristics of wave propagation along a catenary depend on various impedance conditions; i.e., spatial impedance of catenary, impedance of boundaries. In this study, wave propagation along a simple catenary system is studied with arbitrary impedance conditions such as impedance of pantograph, boundary, catenary etc. Seven coupled equations which determine the characteristics of wave propagation along catenary system have been derived and numerically solved. Results demonstrate the role of each impedance condition in the dynamics of catenary system, i.e. the way in which the conditions affect waves on catenary as well as contact force of pantograph. The formulation and suggested solution method can be certainly used for desinging an optimal catenary system for a given pantograph.