The theory of nonlinear stability for a truncated shallow conical shell wit
h variable thickness under the action of uniform pressure was presented. Th
e fundamental equations and boundary conditions were derived by means of ca
lculus of variations. An analytic solution for the critical buckling pressu
re of the shell with a hyperbolically varying thickness is obtained by use
of modified iteration method. The results of numerical calculations are pre
sented in diagrams, which show the influence of geometrical and physical pa
rameters on the buckling behavior.