Elastic-constant measurements, made with the use of a high-precision ultrasonic interferometer, have allowed determination of the susceptibility critical exponent y in the random-field Ising system Dy(As Vi )04. For pure DyVO4 a value 7 = 1.15 + 0.05 was obtained, which is between the values y = 1 for a mean-field system and y = I.25 for a three-dimensional Ising system with nearest-neighbor interactions, and consistent with conclusions reached by previous authors that there is a strong short-range component to the exchange interactions. Random-field samples yielded a significantly higher value, specifically y = 1.79+0.07, consistent with the two-dimensional nearestneighbor Ising value p =and with results of simulations by other authors, but in disagreement with certain scaling-theory predictions. This is the most reliable value obtained thus far for y in a random-field Ising system in three dimensions. Results of optical-birefringence measurements on the ultrasonics samples, along with numerical simulations, show that the measurement of p was not significantly aftected by arsenic-concentration inhomogeneities.