Stresses and deformations in composite cylindrical tubes as a result of combined loading (internal and external pressure, axial load, applied torque) and a temperature gradient through the wall thickness are studied. The composite tubes studied are. in general, long thick-walled cylinders made of arbitrarily oriented-with respect to the tube axis-orthotropic plies. A displacement-based linear elasticity solution is used in the analysis. Classical Laminated Plate Theory (CLPT), which assumes the composite laminate to be in a state of plane stress, does not predict any stresses in the thickness direction; however, in thick-walled tubes, through-the-thickness stresses may not always be negligible. The elasticity solution has shown that, under internal pressure only, in angle-ply and single-ply tubes, the resulting radial stress is virtually independent of the ply fiber orientation. In cross-ply tubes, these stresses show significant differences. In the case of a uniform temperature change only, the nonlinear distribution of the radial stress changes substantially depending on the ply fiber orientation. Another difference between the CLPT and Elasticity Theory for the analysis of cylindrical tubes is found in predicting the maximum twist rate of the cylinder with unbalanced wall laminate. Elasticity Theory has shown that for thick-walled, single-ply cylinders subjected to a uniform temperature change, the maximum twist rate occurs at the ply orientation angle greater than 45-degrees, depending on the wall thickness and the mean radius of the cylinder, as opposed to 45-degrees as predicted by the CLPT. The twist rate in thin-walled tubes subjected to internal pressure only is found to be much greater than in thick-walled tubes, due to the presence of large radial and hoop stresses in thick walls. In multi-layer cylinders, jumps in hoop and axial stresses have been observed at ply interfaces. Their magnitudes are shown to depend upon the angles of fiber orientation.