This article presents an analysis of the free vibrations of a truncated conical thin shell subjected to thermal gradients. The governing equations of the shell are based on the Donnell-Mushtari theory of thin shells. Simply supported and clamped boundary conditions are considered at both ends of truncated conical shell. Temperature loading due to supersonic flow is assumed to vary along the meridian and across the thickness of the shell Hamilton’s principle is used to derive the appropriate governing equations of a conical shell with temperature-dependent material properties. The shell material has a kind of inhomogeneity due to the varying temperature load and temperature dependency of material properties. The resulting differential equations are solved numerically using the collocation method. The results are compared with certain earlierresults. The influence of temperature load on the vibration characteristics is examined for the conical shells with various geometrical properties. © 1996 Taylor & Francis Group, LLC.