Abstract The present study deals with buckling analysis of simply supported conical panels based on the Donnell's shell theory. Different material properties have been considered such as isotropic, composite laminated and functionally graded (FG). The governing differential equation for buckling of laminated conical panel is derived. These equations are discrete using method of discrete singular convolution (DSC). Shannon's delta kernel is used for trial functions. To check the presented DSC method and computer program, the critical buckling loads for isotropic and composite conical panels are calculated which compare very well with earlier available results. The effect of some geometric parameters and material parameters on critical buckling of panels is also investigated. It is noticed that the present DSC methodology can predict accurately the buckling loads of conical panels.