The usual JWKB ray-theoretical description of Love and Rayleigh surface wave propagation on a smooth, laterally heterogeneous earth model breaks down in the vicinity of caustics, near the source and its antipode. In this paper we use Maslov theory to obtain a representation of the wavefield that is valid everywhere, even in the presence of caustics. The surface wave trajectories lie on a 3-D manifold in 4-D phase space (θ, φ, kθ, kφ), where θ is the colatitude, φ is the longitude, and kθ and kφ are the covariant components of the wave vector. There are no caustics in phase space; it is only when the rays are projected onto configuration space (θ, φ), the mixed spaces (kθ, φ) and (θ, kφ), or momentum space (kθ, kφ), that caustics occur. The essential strategy is to employ a mixed-space or momentum-space representation in the vicinity of configuration-space caustics, where the (θ, φ) representation fails. By this means we obtain a uniformly valid Green's tensor and an explicit asymptotic expression for the surface wave response to a moment tensor source.