This paper deals with mechanical buckling of polyethylene/clay nanocomposite beams of functionally graded and uniformly distributed of nanoclay subjected to axial compressive load with simply supported conditions at both ends. The Young moduli of functionally graded and uniformly distributed nanocomposites are calculated using a genetic algorithm procedure and then compared with experimental results. The formulation is modified to include the effect of nanoparticles weight fractions in the calculation of the Young modulus for uniform distribution. Also, it is modified to take into account the Young modulus as a function of the thickness coordinate. The displacement field of the beam is assumed ba- sed on the Engesser-Timoshenko beam theory. Applying the Hamilton principle, governing equations are derived. The influence of nanoparticles on the buckling load of the beam is presented. To investigate the accuracy of the present analysis, a compression study with the experimental results is carried out.