This paper deals with the transient structural response problems. An alternative to the direct integration techniques of transforming the equations of motion into the frequency domain is used. In this paper, the application of finite element-Riccati transfer matrix method is extended from the eigenvalue analysis of structures to transient structural response analysis in the frequency domain. In combination with fast Fourier transform, the finite element-Riccati transfer matrix method in the frequency domain can be used to obtain the transient response of structures. Some numerical examples are proposed and their results are compared with those obtained by direct integration method. Copyright (C) 1996 Elsevier Science Ltd.