An ultrasonic pulse technique has been developed for measuring phase velocity and attenuation spectra in rocks inside a pressure vessel. This technique has been adapted from those used in the nondestructive evaluation field. In essence, a broadband acoustic pulse is directed into a lucite buffer, which is followed by the rock sample and another lucite buffer. The pulse partially reflects off both the front and back faces of the sample, and the reflected pulses are received by the transmitting transducer. Digital recording and signal processing techniques are used to analyze the signal. After Fourier transforming each pulse, correcting for diffraction effects, and allowing for partial reflections at the interfaces, the phase shift between pulses at each frequency yields the phase velocity and the amplitude reduction gives the attenuation. Tests on synthetic materials show that as currently implemented, the technique produces reliable measurements at frequencies above 400 kHz. Velocity and attenuation spectra are shown for brine saturated Massilon and Boise sandstones at different effective pressures.