An expansion procedure using the Chebyshev polynomials is proposed by using El-Gendi method [1], which yields more accurate results than those computed by D.Hatziavrmidis [2] as indicated from solving the Orr-Sommerfeld equation for both the plane poiseuille flow and the Blasius velocity profile. The present results are also more accurate results than those computed by A.R.Wadia & F.R.Fayne C31 as indicated from solving the Falkner-Skan equation, which uses a boundary value technique. This method is accomplished by starting with Chebyshev approximation for the highest-order derivative and generating approximations to the lower-order derivatives through integration of the highest-order derivative.