The clinical objective of Computer Assisted Medical Interventions (CAMI) is to develop systems that assist the physician in the practice of minimally invasive diagnostic or therapeutic actions. The main scientific objectives that result from this clinical goal include the design and development of (1) reconstruction methods, image processing and data fusion, (2) models describing organs and clinical procedures, (3) simulators enabling action planning, monitoring and prediction of outcomes; and finally (4) guiding systems to realize an action as planned. In this CAMI context, biomechanical models of organs and soft tissues can be required to assist surgeons for planning (pre-operative surgical assistance) or to guide their gesture during surgery (intra-operative guidance). The objective of this Perspective Talk is to introduce the state of the art as concerns biomechanics for CAMI. In particular, the main challenges in this area will be addressed and discussed.