Free vibration analyses of beams on elastic foundation are very common in civil and mechanical engineering. Such types of structures are exposed to dynamic loads is a complex soil-structure interaction problem. In the present study for safe and economical design of such structures, a workable approach for free vibration analysis of beams on Winkler foundation using first-order continuity (C1) two degree of freedom (DOF) per node three nodded beam based on Euler-Bernoulli beam theory (EBBT) is attempted. A Matlab code is developed for the present formulation. The results, thus obtained, are compared with similar studies done by other researchers as well as with exact solution where applicable, which show very good conformity and a maximum difference 0.24% with exact solution for mode eight. It is concluded that the present formulation has rapid convergence regardless of boundary conditions, depth to length ratio of beam and modulus of sub-grade reaction. It performs extremely well for thin beams in terms of ease and consistency and gives a very accurate result with only few elements and within few seconds.