An approximate solution of the vibration of an elastically restrained, uniform and non-uniform beams with translational and rotational springs is obtained using Rayleigh-Ritz approach. The frequencies are presented for wide range of restrained parameters and some of these have been compared with those available in the published literature illustrating the accuracy and versatility of the approach. It is believed that the results present in this paper will be of use in design of beams, shaft, and piping under dynamics consideration.