Assuming that the interface of two loosely bonded half spaces permits a finite amount of slip, and that a simple linear relation exists between the prevailing shearing stress and the slip, a generalised secular equation for the Stoneley mode is derived and solved numerically. The two limiting cases of smooth interface and bonded interface are shown to be special cases of this general problem. For some range of values of the elastic constants of the half spaces, unattenuated and undispersed interfacial waves can propagate along the interface only when the interface is smooth or bonded. For the same combination of elastic properties of the half spaces, the loosely bonded interface will cause the interfacial wave to be attenuated and dispersed. The usefulness of this model in relation to the problem of attenuation and dispersion of elastic body waves is briefly discussed.