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In this paper, a new approach is used to study analytically the axisymmetric fluid squeezed between two parallel plates. This new approach depends mainly on the coefficients of powers series resulting from integrating nth order differential equation with known data. We obtianed an analytical-approximate solution for the squeezing flow between two parallel plates. The steady non-linear governing partial differential equations are converted by using the suitable similarity transformation into ordinary differential equation. In addition, some theorems are introduced to prove the convergence of a new approach theoretically and explain the verifications of these theorems computationally. The results domenstrate this new approach is efficient and reasonable which compare with the results of the other methods.

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