We study an elasticity model for compressed protein monolayers or particle rafts at a liquid interface. Based on the microscopic view of hard-core particles with soft shells, a bead-spring model is formulated and analyzed in terms of continuum elasticity theory. The theory can be applied, for example, to hydrophobin-coated air-water interfaces or, more generally, to liquid interfaces coated with an adsorbed monolayer of interacting hard-core particles. We derive constitutive relations for such particle rafts and describe the buckling of compressed planar liquid interfaces as well as their apparent Poisson ratio. We also use the constitutive relations to obtain shape equations for pendant or buoyant capsules attached to a capillary, and to compute deflated shapes of such capsules. A comparison with capsules obeying the usual Hookean elasticity (without hard cores) reveals that the hard cores trigger capsule wrinkling. Furthermore, it is shown that a shape analysis of deflated capsules with hard-core/soft-shell elasticity gives apparent elastic moduli which can be much higher than the original values if Hookean elasticity is assumed.