A solution is presented for the stresses and displacements in an orthotropic, hollow, circular cylinder subjected to asymmetric temperature distribution at the outer surface and heat convection into a medium at zero reference temperature at the inner surface. Assuming temperature-independent material properties, the heat conduction equation in cylindrical coordinates is solved for a single and multilayer cylinders. Results of temperature analysis along with linear elasticity theory are used to obtain the required thermal stresses and displacements. Numerical results are given for a typical fiber-reinforced composite material where fibers in each layer are oriented axially or circumferentially. The results show that the response of the cylinder is sensitive to changes in thickness, orientation of fibers in each layer, number of layers, and stacking sequence.