In this paper, the reflection of an impulse spherical wave by an infinite plane interface separating two fluids is studied. Since both propagation media have a finite acoustical impedance, the boundary conditions at the interface show that the reflected field is distorted and does not show a spherical wave front. Under some particular conditions according to the velocity ratio between the two fluids, it is possible to observe the generation of head waves and/or tail waves. A numerical method is proposed to compute the reflected field based on Fourier transforms over temporal and spatial variables. It will be shown how the reflected field can be reduced to a single integral transform, and how a closed form solution can be obtained in some particular cases. Computations of the reflected field are presented for different values of densities and velocities, illustrating the generation of head waves and tail waves in addition to the expected spherical wave front. Finally, these results are compared to those obtained with the ‘‘impulse ray modeling’’ approach [D. Guyomar and D. Cassereau, Proc. IEEE Ultrasonic Symposium, 731–734 (1987); D. Cassereau and D. Guyomar, in Proceedings of the International Symposium on Acoustic Imaging (Plenum, New York, 1987), pp. 469–481; J. Acoust. Soc. Am. 84, 1504–1516 (1988)], therefore leading to a partial and interesting justification of the ray model.