In this paper, we give an simple but approximate yield surface for single FCC crystals in Hill's criterion form by Schmid's law and nonlinear optimization theory. Assuming that all FCC crystallites in a polycrystal have the same (current) critical resolved shear stress τc for slip, we derive two closed but approximate yield functions through the orientational averaging of all FCC crystallites' yield surfaces in the polycrystal. The effect of crystallography on the two yield functions are described by the orientation distribution function.