Abstract: A Quasi-Flow Theory of elastic plastic finite deformation is proposed. Thetheory originates from the classical normality law. By introducing a weak function withrespect to elastic modulus into the constitutive equations and by improving the commondecomposition scheme of elastic and plaistic strain rates, the Quasi-Flow Theory achieves asmooth and continuous transition from the fiuite deformation Prandtl-Reuss equation (J2F)based on the norrnality law to the rate form of the hypoelastic J2 deformation theory...