Trocar insertion is the first step in Laparoscopy, Thoracoscopy and most other micro surgery procedures. It is a difficult procedure to learn and practice because procedure is carried out almost entirely without any visual feedback of the organs underlying the tissues being punctured. A majority of injuries is attributed to excessive use of force by surgeons. Practicing on cadavers and synthetic tissues may not accurately simulate the process. So there is a need for haptic based computer simulator to train and enhance the trocar insertion skills.For realistic force and torque haptic feedbacks, there is need for realistic modeling of tissue layers and real-time finite element computation. Geometrical complexities of anatomical structures, non-linear complex material properties and their variations with sex, age, person body built, makes patient specific accounting of material properties very difficult. These complexities also make the real time computation of biomechanical models to be prohibitively expensive.In the first half of this thesis a novel method of obtaining patient specific initial conditions, boundary conditions, tissue layers dimensions and their mechanical properties are proposed. A typical patient sample is worked out and cross verified with the available data. In the second half of the thesis, to reduce simulation computation load, a novel method of accounting different tissue mechanical properties by defining tissue specific mapping functions to a single linear function and parallel interpolation of the computation results to the real tissue properties for real-time simulation is proposed.Reduction of Biomechanical Models and Subject Specific Properties for Real-Time Simulation of Surgical Trocar Insertion