The thin airfoil theory for the case of steady,compressible, inviscid,and uniform flow past a Joukowski airfoil located along the horizontal axis is considered. Velocity potential is extended to a second-order approximation. Flow quantities,at the body surface,such as speed,pressure coefficient,and drag coefficient are obtained,up to a second-order approximation,for various values of Mach number "M" less than unity. Approximate value of the critical Mach number in the related compressible flow about the thin airfoil when its section is contracted with the Prandtl-Glauert correction factor,in the stream direction,is calculated. The results are plotted and difficulties in calculations are discussed.