In this paper, soft tissue is modeled by a mass-spring-damper system and tissue deformations under the compression of surgical instruments are simulated. For this purpose, soft tissue confined in a cubic plastic mold is studied using a nonlinear viscoelastic model. Displacements resulting from probe insertions are measured and modeled for use in robotic surgery. Data is collected on bovine sirloin using the Instron hardness tester. The model's dynamic equations are obtained in the form of ordinary differential equations. The external force is considered as the input and the resulting deformation as the output of the model. Simulation results are compared with laboratory findings, and the nonlinear model's unknown parameters are estimated. The threshold force and displacement before the tearing of the soft tissue are respectively determined by analyzing the force-time and displacement-time diagrams obtained for the test samples.