This paper focuses on the damped and undamped transient response of in-plane and out-of-plane loaded stepped curved rods. A unified approach combining the complementary functions method with the Laplace transform is applied to examine the dynamic behavior of above structural elements, while the materials are assumed to be isotropic and homogeneous. The effect of shear deformation is also taken into account. As examples, the forced vibration analysis of a stepped circular arch subjected to step, triangular impulsive and rectified sinusoidal wave in-plane loads and a stepped circular rod under the step, pulse and square wave out-of-plane loads are presented. To validate and compare the results of the present study, two computer programs are coded in Fortran. Verification and exactness of the written programs are performed by comparing the results of the present method and results of ANSYS which is a conventional finite element program. It has emerged that present method is highly accurate and efficient compared to conventional step-by-step integration methods.