Ductile fracture process usually occurs due to the accumulation, growth, and combination of defects or cracks of material and is called ductile Damage. Failure in materials can be predicted, using Damage mechanics and Damage criteria. On the other hand, most of the materials depended on the manufacturing process, are formed in warm or hot conditions so that; the temperature affects on the probable Damage initiation. In this study first, a number of conventional hot forming processes of aluminum alloys such as forming process by tail gas, hydroforming, and blank forming with punch are simulated by finite element method and employing different Damage criteria, and Damage initiation in them is predicted. Then, the obtained numerical results are compared with the experimental results achieved from empirical experiments and validated. Finally, the Damage criteria are classified based on the accuracy of the predicted results and the most appropriate criteria for predicting the Damage in hot forming processes are introduced. It is concluded that Brozzo and Ayada Damage criteria are the most proper criteria for predicting the Damage initiation in the hot forming processes.