The paper presents an analytical method for the analysis of dynamic response of one dimensional structures. In the analysis, the linear partial differential equations and the inhomogeneous boundary conditions that govern the response of the distributed subsystem are Laplace transformed with respect to time, and case into a state space form. The transfer function is determined in an exact and closed form by the state space technique. The transient response is obtained using the inverse Laplace transformation. Numerical examples are provided to illustrate the efficiency of the method.