This thesis is a generalization of the works done by Abdulkawi, Eshkuvatov and Nik Long . We introduce solution of cauchy type singular integral equations of airfoi l. During the last three decades, the singular integral equation methods have been studied. one of the important reason is application of this area at the sevral basic fields such as elasticity, plasticity, fracture mechanics, electromagnetis of antenna, hydrodynamics and aerodynamics. Hence its intersting the first step introduce integral equatio and Chebyshev polynomials properties. then we make mathemathics modeling of airfoils. after this we obtain singular integral equation first kind with a cauchy type singular kernel over a finite interval. if consider kernel zero then its so called airfoil equation. For solving this equation we use from orthogonal Chebyshev polynomial first kind ,second kind , third kind and fourth kind and t he weighted function corresponding with Chebyshev polynomial are At this thesis uses of third and fourth kind Chebyshev polynomial and finally shown identical the exactness of approximation method when the force function is cubic.