The effects of an externally imposed linear shear profile in the Vicsek model of self-propelled particles is investigated via computer simulations. We find that the applied field changes in a relevant way both the equilibrium and dynamical properties of the original model. Indeed, short time dynamics analysis shows that the order-disordered phase transition disappears under shear, because the flow acts as a symmetry breaking field. Moreover, the coarsening of particle domains is arrested at a characteristic length-scale inversely proportional to shear rate. A generalization of the original Vicsek model where the velocity of particles depends on the local value of the density is also introduced and shows to affect the domain formation.Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas