A fiber Bragg grating (FBG) sensor for detection of ultrasonic waves in liquids and solid structures is investigated. The sensor contains a fiber probe with a FBG, a tunable narrowband laser source, and a photodetector. When ultrasonic waves impinge on the fiber probe, the pitch of the grating is modulated through the elasto-optic effect. The corresponding changes in reflectivity of the grating are detected by a photodetector. The sensitivity of the sensor and its frequency and directional response in the 0.5 to 3.0 MHz range are measured. Some anomalous features of the FBG ultrasound sensor response are noted. It is shown that these features result from a combination of the sensor's response to the direct ultrasonic waves propagating through the medium and the signal generated by axially guided ultrasonic waves propagating through the fiber probe.