A theoretical analysis of the buckling of a multilayered thin orthotropic composite circular cylindrical shell of finite length, subjected to (a) uniform axial compression, and (b) axial compression combined with radial pressure, is presented. At each end of the shell, four boundary conditions are satisfied. Four combinations of boundary conditions for simply supported shells, and four combinations of boundary conditions for clamped shells, are treated. These boundary conditions are reduced to the vanishing of a fourth-order determinant. Buckling loads for boron-epoxy composite shells are determined and the results are shown in a series of diagrams. The effect of boundary conditions on the buckling load for various geometrical dimensions of composite cylinders is investigated. Details of the boundary conditions are shown to have strong influence on the buckling load of the shell. The minimum critical axial compression for a simply supported shell with boundary conditions SS1 is as low as 79 percent of the minimum critical axial compression for a shell with classical boundary conditions SS3. As a special case of a composite shell, the minimum critical axial compressive stress for a homogeneous, isotropic, simply supported shell with end conditions SS1 is found to be 43.7 percent of the classical critical stress.