Hooke's law is used to calculate the elastic stress and strain in interstitial magnets. Emphasis is put on spherical and plate-like Sm₂Fe₁₇N_x particles with continuous and discontinuous interstitial concentration profiles, hypothetical high-performance Sm₂Fe₁₇N₃₋₈/FeCo composites, and 'natural' multilayers such as Nd₆Fe₁₃CuH_x, where the recently discovered large anisotropic lattice expansion is shown to arise from the crystal structure.