The state of cure of epoxies is an important issue in the manufacture of graphite epoxy composites used in aerospace structures. Variations in the initial state and process used to cure the epoxy resin in a composite material lead to variations in the mechanical properties of the part manufactured from the composite._[12] Control of these variation can be accomplished by monitoring the bulk and shear moduli of the epoxy resin as it cures. The moduli properties of the resin determine the acoustic properties of the epoxy._{[12],[13],[14]} Hence measurement of the acoustic longitudinal velocity and attenuation of the epoxy during its cure cycle provides a good indicator of the state of cure. Optical fiber waveguides can be embedded within a host material and used to detect longitudinal acoustic waves._[15],[16] Herein, the mechanisms allowing the detection of ultrasound with optical fiber are presented. An analysis of optical fiber waveguides and optical fiber based interferometric detection methods is performed in detail. The interaction of radial strain fields, induced by longitudinal acoustic waves, with singlemode optical fibers is described. Experimental results obtained in epoxy cure monitoring, using an optical fiber based method for acoustic detection, are compared with results obtained using conventional piezoelectric based acoustic detection methods. / Master of Science