Approximate analytical solutions of temperature distributions and thermal stresses, as well as the natural frequencies associated with radial vibrations, in the presence of initial thermal stress, are discussed in this study for thin, circular, cylindrical shells. The problem of temperature distribution is solved approximately by employing the heat conduction equation for a thin rod; the thermal stresses are determined on the basis of a linear stress-temperature relation, and the vibrational frequencies are obtained from Donnell-type equations of motion with the aid of Galerkin's method. Experimental determination of frequencies of a cylinder subjected to axisymmetric line heating at the midsection is reported. Numerical results indicate that the change in frequency induced by thermal hoop stress in a simply supported cylinder is very small except when the cylinder is extremely short and thin. Large changes, however, can be expected for clamped cylinders, and the changes are primarily a result of the presence of a constant axial stress brought about by the temperature increase.