Abstract: A theoretical analysis of boundary layer flow on the continuous moving surface of power law fluids was carried out based on the theory of dimensional analysis of the fluid dynamics. The magnitude and the influencing factor of the laminar boundary layer thickness were obtained. The governing equations of mass and momentum were transformed into the dimensionless form by introducing dimensionless variables. The flow fields of different power-law index fluids with different velocity ratio parameters were presented numerically. The characteristics of the flow and the influence of power-law index and velocity ratio parameter on the flow were analyzed. The results show that the dimensionless velocity and shear stress depend not only on the velocity ratio parameter of the plate, but also on the power law index.