The buckling analysis reported here is for finite-length sandwich cylinders clamped at both edges and loaded in axial compression, pure bending, or a combination of these loadings. Love's first-approximation shell theory is used, and a Rayleigh-Ritz solution is obtained. For axially compressed sandwich cylinders with clamped boundary conditions, the theory predicts values above published experimental results. For pure bending, predicted results are considerably above the experimental results; however, the experimental data represent a very limited number of specimens. Results for pure bending and combined bending and axial compression are in general agreement with published theoretical results for isotropic thin-walled simply-supported cylinders.