This report documents progress made regarding the development and validation of a class of models examining the reliability of nondestructive vibrational inspection tests of single spanned bridges. Two important problems were identified for special consideration. The first concerned the development of a mathematical formulation of the nonlinear boundary conditions needed to accurately model the end support structures of single-span (stringerbased) timber spans. A computational algorithm for the numerical approximations of such systems was derived, implemented and tested with the commonly available Mathematica software package. The second focal problem involved the modeling and analysis of a newly-proposed vibrational testing method. The method seeks to predict bridge strength from vibrational data, and (most importantly) without the need to estimate overall bridge mass. Models developed in this project have provided the first steps towards developing a mathematical understanding of these issues, as well as the creation of a new bridge testing protocol involving the measurement of bridge vibrational responses to forced vibrations both with and without controlled loading. This work has contributed to the development and application of new motion detection sensor technologies addressing the problem of monitoring and estimating bridge integrity.