Surface acoustic wave (SAW) devices find uses in a plethora of applications including but not limited to chemical, biological sensing, and microfluidic actuation. The primary aim of this dissertation is to develop a SAW biosensor, capable of simultaneous detection of target biomarkers in fluid media at concentrations of picogram/ml to nanogram/ml levels and removal of non-specific proteins from sensor surface using the process of acoustic streaming, for potential chemical sensing, medical, and clinical diagnostic applications. The focus is on the development of three dimensional finite element structural and fluid-structure interaction models to study wave propagation and acoustic actuation of fluids in a SAW biosensor. This work represents a significant improvement in understanding fluid flow over SAW devices, over the currently available continuum model of Nyborg. The developed methodology includes use of a novel substrate, namely, Langasite coupled with various combinations of novel multidirectional interdigital transducer (IDT) configurations such as orthogonal, focused IDTs as well as sensor surface modifications, such as micro-cavities. The current approach exploits the capability of the anisotropic piezoelectric crystal to launch waves of different characteristics in different directions, which can be put to the multiple uses including but not limited to sensing via shear horizontal waves and biofouling elimination via Rayleigh wave induced acoustic streaming. Orthogonal IDTs gives rise to constructive interference, thereby enhancing the magnitudes of device displacements and fluid velocities. The net effect is an increase in device sensitivity and acoustic streaming intensity. The use of micro-cavities in the delay path provides a synergistic effect, thereby further enhancing the device sensitivity and streaming intensity. Focused IDTs are found to enhance the device displacements and fluid velocities, while focusing the device displacements and fluid motion at the device focal point, thereby enhancing the SAW device biosensing performance. The work presented in this dissertation has widespread and immediate use for enhancing sensor sensitivity and analyte discrimination capabilities as well as biofouling removal in medical diagnostic applications of SAW sensors. This work also has a broad relevance to the sensing of multiple biomarkers in medical applications as well as other technologies utilizing these devices such as microfluidic actuation.