A stable and accurate deformable model to simulate the deformation of soft tissues is a challenging area of research. This paper describes a soft tissue simulation method that can deform multiple organs synchronously and interact with virtual surgical instruments accurately. The model we used in our method is a multi-organ system by point masses and springs. The organs that anatomically connect to each other are jointed together by high stiffness springs. Here we propose a volume preserved mass-spring model for simulation of soft organ deformation. It does not rely on any direct constraint on the volume of tetrahedrons, but rather two constraints on the length of springs and the third constraint on the direction of springs. To provide reliable interaction between the soft tissues and kinematic instruments we incorporate the position-based attachment to accurately move the soft tissue with the tools. Experiments have been designed for evaluation of our method on porcine organs. Using a pair of freshly harvested porcine liver and gallbladder, the real organ deformation is CT scanned as ground truth for evaluation. Compared to the porcine model, our model achieves a mean absolute error 1.5024 mm on landmarks with a overall surface error 1.2905 mm for a small deformation (the deformation of the hanging point is 49.1091 mm) and a mean absolute error 2.9317 mm on landmarks with a overall surface error 2.6400 mm for a large deformation (the deformation of the hanging point is 83.1376 mm). The change of volume for the two deformations are limited to 0.22% and 0.59%, respectively. Finally, we show that the proposed model is able to simulate the large deformation of the liver and gallbladder system in real-time calculations.