WE PRESENT a model that permits the simulation of the transient response of polycrystalline aggregates to externally imposed loads and temperature gradients. The mechanical response of the constitutive grains includes elastic, Newtonian (linearly viscous), thermal and growth terms. The formulation explicitly accounts for the anisotropy in the elastic, creep, thermal and growth properties of both grains and polycrystals, and describes the time evolution of the overall visco-elastic moduli and of the internal stresses. It also provides, as limit cases, the correct overall elastic, thermal, creep and growth moduli of the polycrystal. The model is applied to analyse the characteristics of irradiation creep and growth in reactor tubes subjected to hydrostatic pressure. The influence of texture, grain anisotropy, grain shape and thermal stresses over the predicted polycrystal response, and especially over the transient regime, is analysed in detail.