Forming of flat sheets into shell conical parts is a complex manufacturing process. Hydrodynamic deep drawing process assisted by radial pressure is a new hydroforming technology in which fluid pressure is applied to the peripheral edge of the sheet in addition to the sheet surface. This technique results in higher drawing ratio and dimensional accuracy, better surface quality, and ability of forming more complex geometries. In this research, a new theoretical model is developed to predict the critical rupture pressure in production of cone cups. In this analysis, Barlat–Lian yield criterion is utilized and tensile instability is considered based on the maximum load applied on the sheet. The proposed model is then validated by a series of experiments. The theoretical predictions are in good agreement with the experimental results. The effects of geometrical parameters and material properties on critical rupture pressure are also studied. The critical pressure is increased with increase in the height ratio, strain hardening exponent, and anisotropy. Higher punch nose radius expands the safe zone. It is shown that the critical pressure decreases for drawing ratios higher than 4.