The elasto-viscoplastic response of irradiated bainitic steels for pressure vessels of light water reactors is described by a multiscale micromechanical model. The model relies on a simplified set of complex constitutive equations describing intragranular flow under a wide range of temperatures, strain rates, and irradiation levels. These equations were themselves partially calibrated by multiscale analyses based on dislocation dynamics calculations, atomistic calculations, and experimental measurements. They include the contribution of jog drag, lattice friction, evolution of dislocation microstructures, and irradiation hardening. The scaling up of these intragranular laws to polycrystalline samples relies on a computational homogenization method which solves the field equations within periodic representative volume elements by means of Fast Fourier Transforms. This computational method proves advantageous relative to the finite element method in handling the complex microstructural morphology of the model required to achieve overall constitutive isotropy. Macroscopic simulations for uniaxial curves under different irradiation levels are first confronted to experimental curves to identify certain microscopic material parameters employed to describe the evolution of the mean-free path of dislocations with deformation. Subsequent comparisons for the evolution of the yield stress, irradiation hardening and the response to sudden strain-rate variations are then reported for a class of steels with various chemical compositions under wide ranges of temperature, loading rate and irradiation level. Good agreement is obtained in all cases. Finally, simulations are employed to explore the influence of the initial dislocation density on the intragranular stress and strain fields. An appreciable influence on the fields is observed during the elasto-viscoplastic transition but not deep in the plastic range.