Cold tube rolling process is one of the current seamless tube manufacturing methods. HPTR (High Pressure Tube Reducer) cold pilgering is the most appropriate and important technique for manufacturing of these tubes. However there are some challenges in manufacturing of seamless tubes with this method. One of the serious problems of this process is micro-cracks in final product. Numerical modeling is a method to predict and reduce these micro-cracks. In current study, damage in HPTR cold pilgering process is simulated by the finite element software ABAQUS. In these finite element simulations, three different subroutines concerning three different damage models, including Lemaitre model, modified Lemaitre model and cumulative damage model are used to predict damage initiation in the process. Considering the type of applied loads that is reverse loading, the selected damage models must have the ability to model the material behavior with combined hardening. For this purpose the damage models in both case of isotropic and combined hardening were implemented. Due to the complexity in derivation of damage equations, an alternative method for derivation has been proposed. One of the important achievements of this research is using a new method to implement modified Lemaitre damage model with combined hardening. This procedure reduced many difficulties and complexities of previous methods. Due to the high computational cost of the simulations, rather than considering symmetry of the process a new method is also proposed to reduce computational cost and process steps. To insure validation of subroutines, several benchmark tests were simulated and obtained results were compared with experimental and numerical results of previous researches. After reviewing and fixing possible errors in HPTR cold pilgering simulation, results were compared with available experimental and numerical results and a good agreement was observed. The results show that three mentioned damage models correctly predict damage distributions but predicted damage by Lemaitre model is more than modified Lemaitre model due to ignoring crack closure effect in compressive loads. In the same models and conditions, the amount of damage resulting from damage models with combined hardening is less than damage models with isotropic hardening. Also results represent that the crack growth is started from the external surface of the tube. Effects of process parameters like tube feed rate and friction coefficients between tools and tube on damage distributions are also investigated. It is shown that changing in friction coefficient of external tube surface which is in contact with rollers have great effect on the amount of resulted damage on tube also it is realized that different tube internal and external friction coefficients cause shear strain in tube that increase damage. According to these results, the least amount of damage appears when the internal and external friction coefficients are the same and small as possible. Increasing tube feed rate also can increase damage in final tube. Finally, the modified Lemaitre model with combined hardening was introduced as the best damage model to prediction of damage in HPTR cold pilgering process. By using the results of this study, it is possible to improve manufacturing process of these tubes in order to reduce the amount of damage in final products. Keywords: HPTR cold pilgering, Seamless tube, Finite element modeling, Damage mechanics