Enumeration search method (ESM) checks all possible combinations of design variables in a bottom-up approach until it finds the global optimum solution for the design conditions. In this paper an optimum design of a multilayered laminated plate made of unidirectional fibre reinforced polymer (FRP) composite subject to uniaxial compression is sought.ESMtogether with classical laminated plate theory (CLPT) has been used to find the lightest laminate for maximizing the buckling load capable of providing structural stability for a set target uniaxial compression load. The choice of the design variables is limited to 4 possible fibres orientation angles (0,90,-45,+45) and the sequence of the laminate, making the problem an integer programming. Experimental and finite element analyses were used to verify the optimum solution. It has been shown that the exhaustive enumeration search method is a powerful tool for finding the global optimum design.