The focus of this paper is on effective elastic properties (i.e., velocities) in three different kinds of dry and fluid-saturated porous media. The synthetic results are compared with the predictions of the Gassmann equation and the tortuosity-dependent high-frequency limit of the Biot velocity relations. Using a dynamic finite-difference approach we observe for Fontainebleau sandstone the same effective elastic properties as with a static finite-element approach. We show that so-called open-cell Gaussian random field models are similar in mechanical properties to Fontainebleau sandstone. For all synthetic models considered in this study the high-frequency limit of the Biot velocity relations is very close to the predictions of the Gassmann equation. However, using synthetic rock-models saturated with an imaginary fluid of high density we can approximately estimate the corresponding tortuosity parameter.