We present modeling and design of an all-optical MEMS Bragg grating (half-pitch of 125 nm) strain sensor for single-fiber distributed sensing. Low optical loss and the use of frequency modulation rather than amplitude modulation, makes this sensor better suited for distributed systems than comparable designs, e.g. Fabry-Perot and Mach-Zender. Also, multiplexing of several sensors with different period gratings, allow sensors to be connected to a single fiber, thereby minimizing cabling and simplifying readout. We show through analytical analysis and finite element modeling (FEM) that large mechanical amplification can be obtained if using an angled double beam micrometer scale MEMS structure, compared to conventional fiber Bragg grating sensors. An optimized design and fabrication process is presented.