This paper investigates the use of embedded optical fiber Bragg gratings to measure strain near a stress concentration within a solid structure. Due to the nature of a stress concentration (i.e. the strong non-uniformity of the strain field) the assumption that the grating spectrum in reflection remains a single peak with a constant bandwidth may not be valid. Compact tension specimens including a controlled notch shape are fabricated with embedded optical fiber Bragg gratings at identical locations but with different gauge lengths. The spectra in transmission varies between such specimens for given loading conditions. This variation is shown to be due to the difference in gauge length. By using the strain field measured on the specimen surface with electronic speckle pattern interferometry and a discretized model of the grating, the spectra in transmission are then verified analytically. Thus, by considering the non-uniformity of the strain field, the optical fiber Bragg gauge functions well as an embedded strain gauge near the stress concentration. Due to the distributed nature of the measurements within a specified gauge length, the optical fiber Bragg gauge has a large potential to measure debonding in fiber reinforced composites.