In this study, the buckling problem of shells consisting of functionally graded materials (FGMs) under uniform compressive lateral pressure is solved at mixed boundary conditions. After creating the FGM models, the basic differential equations of FGM shells under compressive lateral pressure are derived within the scope of classical shell theory (CST). The basic differential equations are solved with the help of Galerkin method and the formula for the lateral buckling pressure is obtained. The minimum values of the lateral buckling pressure are found numerically by minimizing the obtained expression according to the numbers of transverse and longitudinal waves. The accuracy is confirmed by comparing the numerical values for the lateral buckling pressure of homogeneous and FGM shells with the results in the literature. The influences of FGM profiles and shell characteristics on the magnitudes of lateral buckling pressure are investigated in detail by performing specific numerical analyzes.