Non-uniform beam with lengthwise material variation resting on Pasternak foundation is investigated for free vibration. A beam with its material properties and thickness varying linearly along its length is selected for investigation. Euler-Bernoulli beam theory along with Rayleigh-Ritz method is employed for the formulation and the equation of motion is derived by using Hamilton’s principle. Beams with two end conditions i.e., clamped on both ends and simply-supported on both ends are considered for investigation. The results of the current work are validated with established results in literature and new results which illustrate the effect various parameters have on the dynamic response of the beam are furnished. The study revealed that, the material variation, thickness variation and the stiffness of Winkler and shear layer significantly influence the dynamic characteristics of functionally graded beam with non-uniformity.