An efficient dynamic finite element method (FEM) for an elastic body with uniform cross-section was developed. In this method, the finite element mesh is generated in such a way that the body to be analyzed is at first sliced into layers with the same thickness and then each layer is discretized in the same way. The computational time and memory can be saved by utilizing the regularity in the mass, viscosity and stiffness matrices and making them repetitive block tridiagonal matrices, which results from the above mesh. A few example problems were solved with this method to demonstrate its effectiveness. This method is also applicable to many other problems, such as thermal and electrical problems.