The plastic instability of cup-drawing is usually measured by the limiting drawing ratio (LDR). A new and practically applicable equation for estimating the LDR in the cup-drawing of a cylindrical cup with a flat-nosed punch is derived using an integral technique based on the load-maximum principle for localization of the plastic flow. It is a function of the process parameters of normal anisotropy value R̄, strain-hardening exponent n, friction coefficient μ, radius of the die arc rd, half die opening r1 and yield strength σy, and can clearly explore the interaction between the process parameters and the LDR in a theoretical manner. Good agreement between calculation and experiment is obtained. It is thereby possible to better understand and control cup-drawing behavior for optimum press-drawability.