We formulate and apply the homotopy analysis method (HAM) to determine the solution of the nonlinear differential equation governing thin film flow of a generalized second-grade fluid on a vertically moving belt. This problem is also known as the Landau-Levich or drag-out problem, which is the problem of withdrawal of a plate or fiber from a liquid bath. We make use of a modified model that has shear-dependent viscosity and that can predict normal stress differences. The results obtained exhibit the effectiveness and reliability of HAM.