Integral transform methods are very useful for solving problems in ordinary and partial differential equations. Among the integral transform methods, the Laplace transform has been applied to solve a lot of initial and boundary value problems in science and engineering. In this paper, the Laplace transform method was used for solving general wave equations on transmission lines. The model of general wave equations on transmission lines resulted into initial value hyperbolic second order partial differential equation which was transformed into ordinary differential equation by using the Laplace transform method. The method of variation of parameters and the convolution theorem of Laplace transformation was now applied to get the final solution to the problem.