The free surface dynamics of a thin film of a generalized second-grade fluid flowing down a slanted plate subjected to the action of gravity have been studied. A nonlinear evolution equation for the dynamics of the thin liquid film is derived using the long-wavelength approximation. The model allows to investigate the impact of fluid rheology and geometrical parameters on the thin film’s height. The nonlinear dynamics equation is implicitly approximated on a uniform grid by applying the finite volume discretization method, which uses upwind discretization of the flux function and first-order discretization of the time differential term. The investigation reveals that the free surface deformation trends are similar for the Newtonian and non-Newtonian fluids but the non-Newtonian fluid properties substantially influenced the size and shape of the deformation. It is also found that the shear-thinning fluid moves faster down to the plate compared to the Newtonian and shear-thickening fluid.