Abstract The phenomenon of brittle-to-ductile transition (BDT) is known to be controlled by the competition between cleavage fracture and dislocation activity at crack tips, but the transition could be determined by one of the two successive processes, dislocation nucleation or dislocation motion. In this paper a model is developed to study the BDT controlled by dislocation mobility. The model material is assumed to undergo elastic rate-dependent plastic deformation, with the plastic strain rate scaled with dislocation velocity. An isotropic plasticity theory is used. The BDT is assumed to occur when the crack tip is shielded by the surrounding plastic zone such that it never reaches the critical stress intensity for cleavage fracture. The crack tip shielding due to plastic deformation is evaluated using the finite element method. The dimensionless groups that affect the BDT are identified, and a parametric study is performed to reveal the effects of various dimensionless parameters. Numerical results using the specific material properties of Si single crystals are compared with experimental data. Good agreements are obtained. Some interesting features of the BDT behaviour are predicted by our computer simulations which require further confirmation by experimental studies.