We present a physical model for the propagation of chemical and mechanical waves on the surface of vertebrate eggs. As a first step we analyzed the propagation of the calcium wave observed to sweep over the surface of the Medaka egg (Gilkey et al., 1978). It has been assumed that this wave is driven by a mechanism of calcium-stimulated-calcium-release. By formulating this hypothesis mathematically we can use the observed wavefront data to obtain a map of cortical reactivity. This map indicates a gradient of reactivity along the egg: highest in the animal hemisphere and tapering off towards the vegetal hemisphere. The cortex of Xenopus eggs is also capable of propagating a calcium wave (Busa & Nuccitelli, 1985). At about the same time a wave of expansion followed by a wave of contraction sweeps across the egg surface (Takeichi et al., 1984). We have proposed a mechanism for this wave pair based on the physical chemistry of actomyosin gels. The calcium wave activates solation factors which sever some of the actin chains which leads to an osmotic swelling of the gel. Calcium also activates the contractile machinery of the actomyosin system which causes the gel to contract. The contraction lags the swelling because of the nature of the kinetics: solation and swelling is a more rapid process than contraction. By writing the equations for gel expansion and contraction we can mimic the mechanical and chemical wave propagation by a computer simulation. If the model is correct this provides a method for using the waves as a diagnostic of the mechanochemical properties of the egg cortex.