Computational results for steady laminar flow of three different shear thinning fluids lid-driven square cavity are presented. The viscoelastic nature of the fluids is represented by linear and exponential Phan-Thien Tanner (PTT) and Giesekus constitutive models. Computations are based on finite volume technique incorporating non-uniform collocated grids. The stress terms in the constitutive equations are approximated by higher-order and bounded scheme of Convergent and Universally Bounded Interpolation Scheme for the Treatment of Advection (CUBISTA). Effects of the elasticity, inertia as well as constitutive model parameters on the stress and velocity fields, size and intensity of the primary and secondary vortexes are investigated and discussed in detail. Moreover highly accurate benchmark numerical solutions are provided for each considered constitutive model.