Ultrasonic pulse echo measurements on alumina bodies of porosities ranging from 1 to 40% show linear relationships between both the shear and longitudinal velocities and the total porosity. A quadratic relationship is deduced for the dependence of Young's and shear moduli on porosity. The values extrapolated to zero porosity agree reasonably well with results of other works. Poisson's ratio is constant within the limits of the experimental errors. The attenuation of the echoes increases substantially with increasing porosity. When the experimental results are compared with various theoretical models, it is clear that the ``dilute-suspension'' models are incapable of fitting the observations. Among the ``elastic-bound'' models, a cylindrical pore model seems to fit the data much better than a spherical model.

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