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Welding of living tissues replaces stitching of tissues with threads during surgical operations. It simplifies and shortens the time of operation performance, lowers their cost and probability of postoperative complications. Water makes up more than half of the biological tissues mass. During welding the melting stage is not clearly expressed. In the post-operative period the weld should be gradually replaced by a healthy tissue without loss of strength. Computer modeling greatly accelerates, simplifies and lowers the cost of studying the mechanical, electromagnetic and thermal processes, running in live tissue welding. Different mathematical packages allow modeling these processes simultaneously. The paper gives an example of mathematical modeling using the finite element method. Its application enables overcoming the difficulties, when studying the processes running in live tissue welding and allows using a 3D computer model, which models the processes of tissues compression and alternating current passage. [ABSTRACT FROM AUTHOR]