The jet flap shows great potential for high-lift coefficients, CL'S of above 10 having been achieved in test. However, the flowfield is markedly influenced by ground effect, particularly at high lift and strong blowing. The two-dimensional inviscid problem is formulated with the usual linearization of boundary conditions. Four fundamental superposable cases are denned: due to jet angle, thickness, camber, and angle of attack. Using complex variables, and mapping into an auxiliary plane gives a boundary-value problem of the Riemann-HilbertPoincare type. Part of the solution is expressed in closed analytic form and the balance obtained by computer. The numerical method described is speedy and convergent, and is useful for other similar problems. The computer generated solution for a thin flat airfoil at arbitrary angle of attack, jet angle, and jet coefficient is presented graphically. It is in excellent agreement with experimental data, provided there is no wake blockage. Blockage effects are briefly discussed. Other jet flap problems that this method can solve are listed; this includes wind-tunnel wall corrections and cascades.