The paper explores the application of loop eigenvalue elasticity analysis (LEEA) to three models in order to reveal the potential of the method for generating insights about model behavior and to uncover issues in developing the method further. The results indicate that the utility of the method depends upon the character of the model and dynamics involved. In models where the transient behavior is of interest, the method yields insights on par with the pathway participation method, though better tools to link the method to time paths of particular variables is needed. In models involving near-equilibrium oscillation, LEEA is clearly the most powerful, though more efficient computer programs are needed to handle large-scale models. In highly non-linear models exhibiting deterministic chaos, LEEA, being based upon linear concepts, does not appear to yield any insight because the eigenvalues may change substantially even when the mode of behavior appears constant. The paper also describes the set of tools and processes that we have developed and the design for a web-based toolbox to make the methods readily available to a wider audience in the hope that others will join the efforts to develop analytical methods for interpreting model behavior.