Abstract This paper presents an analytical approach to investigate the linear buckling of truncated conical panels made of functionally graded materials and subjected to axial compression, external pressure and the combination of these loads. Material properties are assumed to be temperature-independent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of constituents. Equilibrium and linear stability equations in terms of displacement components for conical panels are derived by using the classical thin shell theory. Approximate analytical solutions are assumed to satisfy simply supported boundary conditions and Galerkin method is applied to obtain closed-form relations of bifurcation type buckling loads. An analysis is carried out to show the effects of material and geometrical properties and combination of loads on the linear stability of conical panels.