The purpose of this paper is to present a methodology to predict vibrations of drilllstrings for oil recovery service. The paper extends a previous model in the literature to include drill collar flexibility utilizing a modal coordinate condensed, finite element approach. The nonlinear effects of drillstring / borehole contact, friction and quadratic damping are included. Bifurcation diagrams are presented to illustrate the effects of speed, friction, stabilizer gap and drill collar length on chaotic vibration response. A study is conducted on factors for improving the accuracy of Lyapunov Exponents to predict the presence of chaos. This study considers the length of time to steady state, the number and duration of linearization sub-intervals, the presence of rigid body modes and the number of finite elements and modal coordinates. The results may be helpful for computing Lyapunov exponents of other types of nonlinear vibrating systems with many degrees of freedom.