A new proposition of the direct problem and the variational finite element method for the potential flow past an airfoil or cascades on an arbitrary streamsheet of revolution are presented in this paper. The general K-J condition,as well as the jump conditions on the artificial boundaries and the periodicity conditions on the downstream boundaries of the cascades,is dealt with as an essential boundary condition.The solution can be formulated without adjusting the outlet flow angle and the circulations of splitting blades or airfoil to satisfy the K-J condition.Thus,the computational efficiency is increased rapidly with an automatic program.