For design and analysis purposes, knowledge of the natural frequencies of vibration for beams is often very important. In this research, a new approximate method of solving the fourth order differential equation of motion for transverse beam vibration was developed. Employing a standard fourth order Runge-Kutta solution technique, the method was generalized to handle most combinations of simple and elastic boundary conditions, varying moments of inertia and axial forces. Comparison of results was made to analytical frequency solutions. One result was verified experimentally.