Ultrasonic wave propagation in a composite consisting of spherical glass inclusions distributed in a random homogeneous manner in an epoxy matrix has been studied in the frequency range of 0.3–5 MHz. The longitudinal and shear phase velocities, and the attenuation of longitudinal waves in the composite were determined as functions of frequency and the volume fraction of the inclusions.The results are compared with several theoretical analyses available in the literature. It is shown that the results of Datta are in very good agreement with the experimental observations. Further, the data satisfy the bounds due to Hashin and Shtrikman, and due to Miller. The phenomenon of cut-off frequencies—a characteristic of periodic composites—is not observed in the random particulate composities.