<p>The paper deals with the effect of thermal preload on snap-through instability of axisymmetric functionally graded shells subjected to external pressure. A finite-element formulation is proposed for geometrically nonlinear analysis of the shells taking into account two-step loading history. At the first loading step, the shell is heated. The corresponding stress–strain state is determined under the assumption of steady-state heat conduction through the wall thickness. At the second step, thermally deformed shell is subjected to uniform inward pressure. To trace the deformation paths, the arc-length control method is employed. Stability of equilibrium configurations is checked by examining the second variation of the total potential energy. Several test problems are solved to validate the proposed finite-element formulation. The effect of temperature field, material properties, boundary conditions, and shell geometry on snap buckling instability of functionally graded shells is studied.</p>