A simplified theory is developed for calculating the creep buckling of components in the form of prismatic bars, and extended to cover the case of two-member components such as reactor fuel elements. The rate modulus (evolved at the mean stress) approach is used and all phases of creep and elastic strains are considered. For the two-member components it is shown that a solution in closed form can only be obtained when the mean stresses in the components remain constant. In general this will not be the case and a graphical method of solution involving isochronous stress-strain curves is suggested. Throughout the analysis a modified form of the Andrade tensile creep equation proposed by Graham and Walles is assumed. Results of creep buckling experiments on E1C-M commercially pure aluminium rods and on magnox A.12 rods are presented, together with data for the creep buckling of composite specimens of the two materials, and compared with the theory.