We report, for the first time, a low cost, compact, and novel mechanically designed extrinsic Fabry-Perot interferometer (EFPI)-based optical fiber sensor with a strain amplification mechanism for strain measurement. The fundamental design principle includes a buckled beam with a coated gold layer, mounted on two grips. A Fabry-Perot cavity is produced between the buckled beam and the endface of a single mode fiber (SMF). A ceramic ferrule is applied for supporting and orienting the SMF. The principal sensor elements are packaged and protected by two designed metal shells. The midpoint of the buckled beam will experience a deflection vertically when the beam is subjected to a horizontally/axially compressive displacement. It has been found that the vertical deflection of the beam at midpoint can be 6-17 times larger than the horizontal/axial displacement, which forms the basis of a strain amplification mechanism. The user-configurable buckling beam geometry-based strain amplification mechanism enables the strain sensor to achieve a wide range of strain measurement sensitivities. The designed EFPI was used to monitor shrinkage of a square brick of mortar. The strain was measured during the drying/curing stage. We envision that it could be a good strain sensor to be embedded in civil materials/structures under a harsh environment for a prolonged period of time.