Surface acoustic wave (SAW) devices are finding increasing use in medical diagnostic applications, such as detection of specific proteins in bodily fluids for detection of pathologies. These devices can also be used in Lab-On-a-Chip devices for biological applications that utilize micro-fluidics for detection, transport, mixing, and biological assays. In applications aimed at biological sensing, the sensing medium such as blood exhibits a non-Newtonian behavior. In biosensing applications of SAW devices, SAW induced acoustic streaming which refers to fluid motion induced by high frequency sound waves, is an important phenomenon that can be used for the removal of non-specifically bound proteins from the device surface. Acoustic streaming also finds use in a wide variety of other applications such as detection of ovarian cysts and detection of blood clotting via ultrasound and convective transport in microfluidic applications of SAW devices. This work reports on the influence of non-Newtonian fluid dynamics on the acoustic streaming and fluid velocity profiles in SAW devices, using a computational fluid-structure interaction finite element model.