There currently exists no reliable, non-destructive method for measuring stress in railroads and other similar structures without the need for a calibration measurement. Major limitations which have hindered previous techniques include sensitivity to boundary conditions, insensitivity to stress, and intolerance for material and geometry uncertainty. In this work, a technique is developed which seeks to solve these challenges by extracting the spectrum relation, or dispersion curve, of a waveguide from dispersive wave propagation meaasurements. The technique is based on spectral analysis of waves in structures modeled as beams, and as such is based on relatively low frequency vibrations, as opposed to other techniques which use nonlinear elastic modeling of structures at ultrasonic frequencies. The major contribution of this work is the development of a frequency-domain based signal processing technique which is capable of compensating for the dispersive, long wavelength reflections which have limited the ability of previous techniques to go low enough in frequency to achieve high stress sensitivity. By compensating for reflections, the present work is able to automate the process of analyzing wave propagation signals such that the entire dispersion curve can be extracted, enabling the identification of various parameters including stress, stiffness, density, and other material and geometry properties. This in turn enables measuring stress, performing model-updating for material and geometry uncertainty, and being indifferent to boundary conditions. The theory and algorithmic implementation is presented, along with simulations and experimental validation on a rectangular beam. / Master of Science / The ability to detect damage or the potential for damage in structures is highly desirable, especially in industries such as civil infrastructure in which failure can be incredibly costly and dangerous. In particular, non-destructive techniques which can predict failure without interfering with the operations of a structure are particularly sought after. In this work, a technique for non-intrusively and non-destructively measuring stress is developed, with the primary application being for measuring stress in railroads. The technique seeks to advance the state-of-the-art in wave-propagation-based techniques by adding the capability to automatically identify reflected waves. With this new capability, the method is able to quickly and efficiently analyze a large set of vibration measurements to extract information about the structure's material, geometry, and loading characteristics which enables solving for stress even when the structures material, geometry, and boundary conditions are not precisely known. The technique is demonstrated on both simulated and experimental data, in which a rectangular beam is tensioned and the stress is then identified.