Annotation: This article is devoted to the study of behavior of shallow thin-walled conical shells under action of combined load of uniform normal pressure and concentrated force in case of non-homogeneous stress-strain state (SSS). The type of combined load on the shallow conical shells (that have widespread use as roofs and couvertures of reservoirs) represents conditions of exploitation and consists in simultaneous action of snow load and weight of human who may change its position in space and located on the surface of shell. The behavior of shell has been modelled using software ANSYS 14.5 either during linear static stability calculation (buckling) or geometrically non-linear calculation of deformation of shell.