The paper shall proceed to describe a model tree and its material properties and explain the finite element model used. It shall then provide a simplified model that was tested for agreement with a mathematical solution. The paper shall then proceed to explain results obtained from finite element modeling. Natural frequencies for the first 25 modes shall be shown. The evolution of mode shapes shall be illustrated for both increasing frequencies as well as decreasing element size. The undamped response of the model tree shall be shown for a particular harmonic frequency and then the damped response shall be shown over a range of driving frequencies. Finally, the effect of rigid end zones shall be explored in more detail, combining the approaches from the previous sections to show the importance of rigid end zones.