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Domain switching around electrically permeable and impermeable cracks in ferroelectric single crystals subjected to a mechanical load is investigated by using a phase field model.It is found that the electrical boundary conditions have little effect on the polarization distribution without any external load when the initial polarization is parallel to the crack,which is totally different from previous studies where the initial polarization is perpendicular to the crack.However,the simulation results show that the electrical boundary conditions have great influence on the polarization distribution as well as the domain switching behavior when a mechanical load is applied.The critical mechanical load of domain switching with a permeable crack is much smaller than that in the case of an impermeable crack.