In this article finite differences are used to study viscoelastic incompressible flow of a Criminate Erickson Filbey fluid in a square cavity flow domain. In this case, the nature of corner singularities is examined in which the fluid is contained and the flow generated by the motion of one or more walls. The governing equations are formulated in terms of stream function and vorticity equation and the corresponding radial parts are defined by a fourth-order non-linear differential equations for Stokes flow. In recent years that mathematical formulations of viscoelastic flows -often remain very complex velocity and stress field and then stress singularities are known to occur in several flows as in this article. Therefore, singularity behaviour became a very important current issue in fluid dynamics. However, this article is set up with the aim of examining the corner, singularities for cavity driven flow in 2D for viscoelastic flow despite the Newtonian flow being well known. Then we show that the viscoelastic fluid has different singularity behaviour than the viscous fluid near the corner with respect to the shear-rate.