hased on both the wrinkle model and fracturc model, the wrinkle critical tangent pressure and the fracture on critical radial tensile stress are calculated respectively. The maximum tangent pressure formula in the flange deformation zone and the maximum radial tensile stress formula in the cylinder-wall pass force zone are given, and both the no-wrinkle limitl criterion and no-fracture limit criterion are put froward. The prediction and control criterion and diagram of both the wrinkle limit and fracture limit on cylindrical cup deep-drawing, the most suitable forming zone and the limit deep-drawing coefficient are obtained. Comparing with present experience formulae and actual product's production, this prediction and control are quite accurate.