A model as developed based on the time-related thermal diffusion equations to investigate the effects of two-dimensional shear flow on the stability of a crystal interface in the supercooled melt of a pure substance.Similar to the three-dimensional shear flow as described in our previous paper,the two-dimensional shear flow can also be found to reduce the growth rate of perturbation amplitude.However,compared with the case of the Laplace equation for a steady-state thermal diffusion field,due to the existence of time partial derivatives of the temperature fields in the diffusion equation the absolute value of the gradients of the temperature fields increases,therefore destabilizing the interface.The circular interface is more unstable than in the case of Laplace equation without time partial derivatives.The critical stability radius of the crystal interface increases with shearing rate increasing.The stability effect of shear flow decreases remarkably with the increase of melt undercooling.