This paper discusses the problem of designing a pile foundation in a multi-layered soil that optimizes the buckling load, taking into consideration the stiffness and frictional resistances of the soil strata. The optimality criteria method was applied in the context of Rayleigh’s quotient, and solved for by variational principles with associated boundary conditions. The results revealed the minimum buckling load of the tapered pile on the multi-layered soil, the resultant effect on the elastic boundary condition. A numerical illustration is presented to emphasize the impact of the pile's tapering and shaft friction, soil non-uniformity, pile-soil stiffness, and the boundary condition at both ends of the pile. It is expected that the study will furnish geotechnical and structural engineers with a tool to easily predict strength improvements in pile foundations from any known layered soil medium.