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This paper performs a theoretical and experimental analysis of the pressure sensitivity of Brillouin frequency shift (PSoBFS) in silica optical fibers with double-layer polymer coatings. It is predicted numerically that the coated fibers have enhanced (ideally over 20 times) PSoBFS as compared with a bare fiber. In addition, the enhancement becomes obvious while the outer coating has a lower Young's modulus and Poisson's ratio, as well as larger thickness. Three fibers with different outer coatings are experimented via the Brillouin optical time domain analysis technique. The experimental results agree with the theoretical prediction. This quantitative evaluation can be guidable for designing BFS-based pressure sensors with coated fibers.