The paper describes a matrix method by which relatively simple expressions may be obtained for calculation of transient-voltage distribution in a system consisting of a transmission line and a transformer winding in series arrangement, subjected to a voltage surge given by an arbitrary function of time. The theory is derived for an equivalent circuit built up of two different uniform ladder networks, each having a finite number of sections. The ladder networks chosen are those usually employed to represent transmission lines and transformers. The differential equations for the transient voltages are compounded into a single matrix equation, the solution of which is obtained using the Laplace transform and the matrix-inversion technique of Shermann-Morrison and Bartlett.