Interfaces that are coated with a layer of adsorbed particles (particle "rafts") are common in natural and industrial settings. Particle-coated interfaces may be useful in part because the particulate structure can endow the fluid interface with physical properties distinct from molecular surfactants. We study the mechanics of particulate assemblies by measuring the raft's response to indentation in the vertical direction by a flat, circular disc. We measured force (f) vs. indentation depth (δ) and found two linear regions with different slopes. The first linear region started at δ = 0 and persisted over a range of δ much less than the capillary length. In the second linear region, the raft had the same stiffness (df/dδ) as a liquid interface with no particles. Further, we show that, as long as the indenter was larger than a single particle, the azimuthal compression imposed by the interface deformation relaxed through in-plane rearrangement of particles rather than by the radial wrinkles that are characteristic of thin elastic sheets at fluid interfaces. We show how the force-displacement curves and stiffnesses depended on fluid mass densities, interfacial tensions, and indenter radius. For all cases studied, the particle-raft coated interfaces had a stiffness equal to or smaller than that of a bare fluid interface. Although the interfacial particle raft behaved like a pure fluid interface under a wide range of displacements, we show that the raft could nonetheless withstand substantially greater applied force (up to 2×) and greater indentation depth (up to 2.6×), so that the range of reversible behavior was greatly extended. These results improve our understanding of the mechanics of particulate assemblies at interfaces.