We have developed a solid mechanics model of nearly incompressible, viscoelastic soft tissue for finite element analysis (FEA) in MATLAB 7.2. Newmark's method was used to solve the finite element equations of motion for our model. The solution to our dynamic problem was validated with a transient dynamic analysis in ANSYS 10.0. We further demonstrated that our MATLAB FEA qualitatively agrees with those results observed with acoustic radiation force methods on soft tissues and tissue-mimicking materials. We showed that changes in Young's modulus and the damping coefficient affect the displacement amplitude and phase shift of the response data in the same manner: An increase in Young's modulus or damping coefficient decreases both the displacement amplitude and response lag. Future work on this project will involve frequency analysis on response data and studying the initial transient region to help uncouple the effects of Young's modulus and damping coefficient on response characteristics. This will get us one step closer to being able to explicitly determine Young's modulus and the damping coefficient from the temporal response data of acoustic radiation force methods, which is the ultimate goal of our project.