The finite analytic method is used in the present study to calculate the turbulent flow field described with Navier-Stokes equation in body-fitted curvilinear coordinate system The finite analytic method invokes the analytic solution of governing partial differential equation in formulating the algebraic equation that relates a nodal value in an element to its neighbour nodal values according to the direction and the magnitude of convection. It is shown that the finite analytic method has good numerical stability and accuracy. The turbulent flow fields through a single and a tandem cascades of airfoil are numerically simulated by using finite analytic method respectively in this paper. The k − ϵ turbulence model and wall function are employed in. the present study. The agreement of numerical solution with experiment result is quite good.