In this study, the buckling analysis of cylindrical shells made of functionally graded materials (FGMs) under the torsional moment resting on the Pasternak-type soil is performed. After establishing the linear constitutive relations of FGM cylindrical shells within the framework of the modified Donnell type shell theory, the governing equations of FGM cylindrical shells under the torsional moment are derived considering the influence of Pasternak-type soil. Analytical formula for the torsional moment is obtained by choosing the approximation functions that satisfies the boundary conditions in an integral sense. From the obtained formula, the formulas for the critical torsional moment in the presence of Winkler soil and absence of soils are obtained as a special case. Variations of critical torsional moment for different soil coefficients, volume fraction ratio and shell characteristics are investigated in detail. Keywords: functionally graded materials; cylindrical shell; buckling; critical torsional moment; Pasternak-type soil.