Accurate knowledge of biomechanical characteristics of tissues is essential for developing realistic computer-based surgical simulators incorporating haptic feedback, as well as for the design of surgical robots and tools. As simulation technologies continue to be capable of modeling more complex behavior, an in vivo tissue property database is needed. Most past and current biomechanical research is focused on soft and hard anatomical structures that are subject to physiological loading, testing the organs in situ. Internal organs are different in that respect since they are not subject to extensive loads as part of their regular physiological function. However, during surgery, a different set of loading conditions are imposed on these organs as a result of the interaction with the surgical tools. Following previous research studying the kinematics and dynamics of tool/tissue interaction in real surgical procedures, the focus of the current study was to obtain the structural biomechanical properties (engineering stress-strain and stress relaxation) of seven abdominal organs, including bladder, gallbladder, large and small intestines, liver, spleen, and stomach, using a porcine animal model. The organs were tested in vivo, in situ, and ex corpus (the latter two conditions being postmortem) under cyclical and step strain compressions using a motorized endoscopic grasper and a universal-testing machine. The tissues were tested with the same loading conditions commonly applied by surgeons during minimally invasive surgical procedures. Phenomenological models were developed for the various organs, testing conditions, and experimental devices. A property database—unique to the literature—has been created that contains the average elastic and relaxation model parameters measured for these tissues in vivo and postmortem. The results quantitatively indicate the significant differences between tissue properties measured in vivo and postmortem. A quantitative understanding of how the unconditioned tissue properties and model parameters are influenced by time postmortem and loading condition has been obtained. The results provide the material property foundations for developing science-based haptic surgical simulators, as well as surgical tools for manual and robotic systems.