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The pulsed elongation of fiber Bragg gratings is considered in order to be used to measure the displacement or deformation rate of objects. Optimal measurement modes were determined, numerical simulation of the output signal was performed during pulsed elongation or compression of the fiber grating, and the main patterns were analyzed. The results of the application of the Bragg gratings for the experimental determination of the deformation rate of materials under pulsed magnetic action are presented. Experimentally obtained and theoretical dependencies are compared. The dependencies of the change in the grating parameters—the coefficient and the half-width of the reflection spectrum with successive shortening of the grating—are given.