The finite analytic method is used in the present study to calculate the turbulent flow field described with Navier-Stokes equations in body-fitted curvilinear coordinate system.The finite analytic method invokes the analytic solution of governing partial differential equations in formulating the algebraic equations that relates a nodal value in an element to its neighbouring nodal values.The major feature of the finite analytic method is its ability to simulate automatically the upwind influence of neighbouring nodal values according to direction and magnitude of convection.It is shown that the finite analytic method has good numerical stability and accuracy.The turbulent flow fields through a two-dimensional channel and a cascade of airfoil are numerically simulated by using finite analytic method in the present study.The k-ε turbulence model and wall function method are also employed.The agreement of numerical solution with experimental data is quite good.