Alzheimer's disease (AD) is an incurable, debilitating neurodegenerative disease affecting millions of elderly people worldwide. Though the exact mechanism of the causation of the disease still remains unknown, early diagnostic methods can certainly help in pinpointing the timeline and progression of the disease. In this regard, biomarker sensors are reliable candidates which provide quicker analysis times and accurate diagnosis. Mass based micro-electromechanical systems (MEMS) biosensors, with increasing versatility and functionality are being radically implemented in biomedical device industry. A thorough understanding of the mechanics and dynamics of the biosensor under various operating conditions are absolutely essential to predict and improve the performance of the biosensor. A MEMS biosensor incorporating mass based resonance frequency shift detection and evanescent wave based fluorescence signal detection achieves dual mode of detection and higher reliability. In this thesis, a finite element based computational approach including fluid-structure interaction is developed for the sensor geometry and the dynamics of the sensor under various fluid conditions and damping mechanisms are explored. Spatially localized parameterized point masses are attached to simulate the effect of biomarker attachment to the beam sensing surface and frequency response of the sensor is analyzed. Monolithic and partitioned approaches for solving coupled physics problems are designed and analyzed. The results obtained from finite element simulations are compared against experimental data obtained from AFM calibration measurements and analytical model. Some approaches towards optimization of the performance of the biosensor with real world clinical applications are also explored.