AbstractA numerical approximation is taken to the solution of the complex flows existing in gas turbine engines with transonic blading. The quasi‐3D approach decouples the problem into through‐flow and blade‐to‐blade solutions. An industrially practical finite element through‐flow solution is developed and for blade‐to‐blade solutions a transonic finite areas method is utilized. The finite element code developed is capable of operating in an analysis or a design mode. In both modes a dynamic relaxation factor is employed and considerable reduction in solution time can be achieved. Comparisons to streamline curvature methods are carried out for simple analytical and complex indust