In this paper, we study the variation of natural frequencies for thin walled circular cylindrical shells subject to external radial load (uniform and hydrostatic pressure). The study has been performed for four different types of boundary conditions viz. pinned-pinned, pinned-free, clamped-free and one end is pinned and other end axially constrained. Towards this, we have used approximate shape functions and Galerkin projections of the PDEs governing the shell motion, linearized about a steady state solution due to the applied mean radial pressure. Our results have very good agreement with the experimental and theoretical results available in literature. They have also been verified against finite element analysis (FEA) using ABAQUS. We have found that with increasing magnitude of inward radial load, the natural frequency decreases, however, the circumferential wavenumber corresponding to the lowest natural frequency increases. For outward radial load the opposite happens. Furthermore, the circumferential wavenumbers corresponding to lowest natural frequency and first buckling mode are different for short cylinders with the difference decreasing with increasing length of the cylinder. We have also found an interesting result for the beam mode vibration of cylindrical shells. For short cylinders, the natural frequency of the beam mode increases (decreases) with internal (external) pressure, which is consistent with other circumferential modes. Subsequently, we obtain a critical length at which the applied radial pressure has no effect on the natural frequency. For cylinders longer than the critical length, the effect of the radial load is opposite of that observed for the short cylinders, and this is contrary to the behavior of the other circumferential modes. As a result, buckling of the beam mode happens for an outward radial (internal) pressure. © 2017 Elsevier Ltd