This paper intends to predict the best lamination stacking sequences for the web and both flanges of cantilever double-tapered beam exposed to an externally uniformly distributed force to achieve the maximum lateral buckling capacity with optimized mass and material cost. Vlasov’s model along with the classical laminated plate theory is utilized for extracting the variational formulation in terms of lateral displacement and angle of rotation due to torsion. Considering a specific member, the Ritz method is employed to derive an analytical expression for the transverse buckling load as an explicit function of stiffness components. Through the technique of genetic algorithm, the optimum design of a lightweight multi-layer fibrous composite I-shaped beam with varying cross-sections that can sustain the maximum lateral buckling load is finally attained. The numerical results reveal that the endurable lateral buckling load of a selected model increases by about 56% via the proposed optimization process.