We demonstrate the possibility of using radio-frequency modulation spectroscopic techniques for interrogation of fiber Bragg-grating (FBG) structures. Sidebands at 2 GHz are superimposed onto the output spectrum of a 1560-nm DFB diode laser. The power reflected by an FBG is demodulated at multiples of the sideband frequency. The sideband-to-carrier beat signal is shown to be extremely sensitive to Bragg wavelength shifts due to mechanical stress. Using this method, both static and dynamic strain measurements can be performed, with a noise-equivalent sensitivity of the order of 150 nepsilon/ radicalHz, in the quasi-static domain (2 Hz), and 1.6 nepsilon/ radicalHz at higher frequencies (1 kHz). The measured frequency response is presently limited at 20 kHz only by the test device bandwidth. A long-term reproducibility in strain measurements within 100 nepsilon is estimated from laser frequency drift referred to molecular absorption lines.