A general solution for the stress and strain fields in a three-layer composite tube subjected to internal and external pressures and temperature changes is first derived using thermo-elasticity. The material in each layer is treated as orthotropic, and the composite tube is regarded to be in a generalized plane strain state. A three-layer ZRY4-SiCf /SiC-SiC composite cladding tube under a combined pressure and thermal loading is then analyzed and optimized by applying the general solution. The effects of temperature changes, applied pressures, and layer thickness on the mechanical behavior of the tube are quantitatively studied. The von Mises’ failure criterion for isotropic materials and the Tsai-Wu’s failure theory for composites are used, respectively, to predict the failure behavior of the monolithic ZRY4 (i.e., Zircaloy-4) inner layer and SiC outer layer and the composite SiCf /SiC core layer of the three-layer tube. The numerical results reveal that the maximum radial and circumferential stresses in each layer always occur on the bonding surfaces. By adjusting the thickness of each layer, the effective stress in the three-layer cladding tube under the prescribed thermal-mechanical loading can be changed, thereby making it possible to optimally design the cladding tube.