An account is given of a study of free vibrations of a simply-supported beam with non-linear material properties. The material is of the Ramberg-Osgood type. Non-linear programming technique was used to find the response of the system. The variation of frequency with amplitude has been obtained for different values of material properties. The results indicate that the beam behaves like a soft spring for the type of non-linearity introduced by the material. This method can be used for all modes directly without reference to the lower modes.