Abstract: The specific problem to be considered here concerns the boundary layer problem of a non-Newtonian fluid on a flat plate in length, whose surface has a constant velocity opposite in the direction to that of the mainstream with U_W>>U_∞ or alternatively when the plate surface velocity is kept fixed but the stream speed is reduced to zero. A theoretical analysis for a boundary layer flow is made and the self-similar equation is determined. Solutions are presented numerically for special power index and the associated transfer behavior is discussed.