Interface waves on a single fracture in an elastic solid are investigated theoretically and numerically using plane wave analysis and a boundary element method. The finite mechanical stiffness of a fracture is modeled as a displacement discontinuity. Analysis for inhomogeneous plane wave propagation along a fracture yields two dispersive equations for symmetric and antisymmetric interface waves. The basic form of these equations are similar to the classic Rayleigh equation for a surface wave on a half-space, except that the displacements and velocities of the symmetric and antisymmetric fracture interface waves are each controlled by a normalized fracture stiffness. For low values of the normalized fracture stiffness, the symmetric and antisymmetric interface waves degenerate to the classic Rayleigh wave on a traction-free surface. For large values of the normalized fracture stiffness, the antisymmetric and symmetric interface waves become a body S wave and a body P wave, respectively, which propagate parallel to the fracture. For intermediate values of the normalized fracture stiffness, both interface waves are dispersive. Numerical modeling performed using a boundary element method demonstrates that a line source generates a P-type interface wave, in addition to the two Rayleigh-type interface waves. The magnitude of the normalized fracture stiffness is observed to control the velocities of the interface waves and the partitioning of seismic energy among the various waves near the fracture. ¿ American Geophysical Union 1996