The yield characteristic and the plastic flow direction of a polycrystal copper are investigated, in which the anisotropy and random orientation of each grain in the polycrystal are taken into account, while the microstructure evolvement and the slip deformation mechanism are also analyzed. Applying the crystal plasticity theory associated with representative volume element (RVE) of a polycrystal aggregate, which consists of 200 polyhedral grains with irregular shape and orientation, the plastic deformation of polycrystalline copper is calculated through applying biaxial load along different paths to the RVE aggregate, stage by stage to simulate the material's biaxial stress state and the sub-stage load path. Then the yield surface and the subsequent yield surface for the RVE under preloading are obtained by the simulation through FEM calculation with the user crystalline material subroutine. The calculation results of the subsequent yield surface shape and the plastic flow direction are resolved and are discussed further. According to the results of yield surface and plastic flow direction of the polycrystal RVE, it can be concluded that the corner may appear on the subsequent yield surface at the preload point and the corner's appearance is dependent on the yield definition and the preload direction on the $\pi$ plane; the classical normality description for plastic flow is proved to be reasonable for the polycrystal aggregate but there is a difference between the flow direction and the surface normal vector, which is analyzed by statistical calculation, and the statistical difference between the plastic flow direction and the normal vector of subsequent yield surface is related with both the yield definition and direction of preloading.