Strain has been proposed as a potential tool to increase the oxygen ion conduction in oxides. Here we study by means of molecular dynamics simulations the influence of isotropic and biaxial strain on the proton conductivity of yttrium-doped barium zirconate to examine whether a similar influence occurs for hydrogen diffusion. Compressive isotropic pressure is indeed shown to favour proton diffusion by diminishing the oxygen-oxygen distance without affecting the symmetry. For moderate biaxial strain, a similar effect is observed i.e. a slight increase of proton conductivity occurs under compressive strain. High biaxial compressive/negative strain leads to a decrease in proton diffusion by inducing a symmetry breaking that results in a strong localisation of protons away from the B cations. The results are discussed and compared with previous DFT calculations and experimental results.