We present submillimeter- and millimeter-wave maps tracing the molecular gas and dust around the edge of the H II region M8. The molecular material is clumped into cores on the scale of the beam (about 0.1 pc) whose temperatures can be estimated from CO observations. The masses of the clumps, estimated from their continuum fluxes, are consistent with a power-law mass function with index -1.7+/-0.6, which agrees with determinations for other molecular clouds at similar resolutions, using molecular lines as tracers. The submillimeter clumps are sited at the interface between the H II region and the background molecular cloud, where they are exposed to the ultraviolet flux of OB stars. The physical parameters of the clumps are compared to published models of molecular clouds undergoing photoevaporation, suggesting that the pressure of the ionized gas exceeds the internal pressure of the clumps and, therefore, that a shock front will be driven into the clumps. The clumps themselves currently appear to be gravitationally unbound, but the compression may be sufficient to induce collapse.