In this study, for the first time, tactile detection of an artery in tissue and distinguishing it from the tumor has been modeled by finite element method. In this modeling, three 2D models of tissue have been created: tissue, tissue including a tumor, and tissue including an artery. After solving three models with similar boundary conditions and loadings, first, the 2D tactile mappings and stress graphs for upper nodes of models, which have the role of transferring tactile data, have been explored. Comparing these results, if stress values of nodes are equal and constant, tissue is without tumor or artery. In addition, it was concluded that if stress graph includes a peak, the tissue has a tumor or an artery and that the stress graph of tissue including artery is time-dependent in comparison with the tissue including the tumor. Then, effect of variation of model's different parameters including tissue thickness, artery diameter and elastic module, and indentation of tactile finger on artery detection was studied.