Abstract: In the present paper, the compatibility equation for the plane stress problems of power-law materials is transformed into a biharmonic equation by introducing the so-called complex pseudo-stress function, which makes it possible to solve the elastic-plastic plane stress problems of strain hardening materials described by power-law using the complex variable function method like that in the linear elasticity theory. By using this general method, the close-formed analytical solutions for the stress, strain and displacement components of the plane stress problems of power-law materials is deduced in the paper, which can also be used to solve the elasto-plastic plane stress problems of strain-hardening materials other than that described by power-law. As an example, the problem of a power-law material infinite plate containing a circular hole under uniaxial tension is solved by using this method, the results of which are compared with those of a known asymptotic analytical solution obtained by the perturbation method.