A model for the thermo-elasto-plastic mechanical behavior of highly textured polycrystals is described. A finite number of grain orientations and equal strain for each orientation are assumed at each unit volume of the ensemble. Some characteristic anisotropic mechanical properties of zirconium alloys, such as the thermoelastic expansion, the dimensional instability under irradiation, and thermal and radiation creep, are qualitatively and semi-quantitatively reproduced by the model. This is obtained, within a microstructural approach, by a rate theory description of the prismatic network dislocation climbing and grain boundary defect absorption or emission at each grain. Homogeneous stress-strain cases as well as nonhomogeneous states are calculated, the latter ones in specimens with cylindrical symmetry. The case of a fuel cladding with internal pressure is studied. Viscoelasticity, thermal creep, creep under irradiation, different creep stages, and creep strength differential under tension and compression are predicted by the model and the phenomena can be correlated with the specimen texture, temperature, and development of intergranular stresses during the test. The importance and necessity of including a microstructural material model for describing the mechanical behavior of stressed zirconium alloy pieces under irradiation are pointed out throughout the work.