AbstractThe paper deals with the propagation of shock waves at the surface of soils. Heterogeneity and damping are introduced into analytical half‐space solutions. The suggested model explains two phenomena, often observed with shock propagation in actual soils, that differ from the behaviour of the homogeneous half‐space: the pronounced decay of the disturbances with distance and the elongation of the disturbance into a train of waves. The effects of heterogeneity and damping are discussed quantitatively.The response of footings on heterogeneous soils has been investigated by several authors. Awojobi4considered the Gibson soil in which the shear modulus increases linearly with depth. Luco5and Gazetas and Roesset6investigated a multi‐layered soil, the shear modulus being constant within each layer. Gazetas7, using a technique suggested by Gupta8extended this method to layers with linearly varying shear modulus. Little work is available on the propagation of waves in heterogeneous bodies. Some results concerning the modes and the mode shapes in heterogeneous soils were reported by Ewing, Jardetzky and Press9and Bath.10The modes have to be superposed in an appropriate way to obtain the displacement field at the surface. This has been approximately achieved by the finite element formulations of Lysmer,11, Lysmer and Waas12and Waas.13Auersch14applied this method to a homogeneous layer on a rigid base. He found some dispersion of the Rayleigh wave within a narrow frequency range. Finite elements combined with discrete Laplace transforms, however, consume much computer time. Rao and Goda15and Rao16calculated surface vibrations of a half‐space with exponentially varying shear modulus and density. Their method is similar to Lamb'S1procedure for the homogeneous half‐space. Only one mode–the Rayleigh wave–occurs in their heterogeneous half‐space. The examples show the considerable effect of heterogeneity on wave propagation. In the present paper, more general variations of the shear modulus