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In this paper, a simple and efficient analysis technique, Hankel-Pade method, is proposed to find the solution of anonlinear ordinary differential equation that appears in the studyof the steady flow of the third-grade fluid in a porous halfspace. The numerical solutions  for some cases of the model'sparameters are obtained by using Hankel-Pade method. Theconvergence of the Hankel sequences is analyzed. Comparison toother available results for these problems reveals reliability andhigh accuracy of the proposed technique. Also the simpleanalytical expressions of the solutions of the governingnon-linear boundary-layer problems are developed as rationalapproximation solutions. The effectivity and convergence of therational approximation solutions are investigated by theillustrative graphs and tables.