A theory of the impurity-induced interatomic forces between atoms of a metal host is formulated in terms of the linear response function of the inhomogeneous electron gas containing a dissolved atom, hydrogen in the present case. Asymptotic properties of the response function, reflecting the presence of a both bound and scattered electronic states, are analysed. Numerically results are shown for a simplified model of the hydrogen impurity in a simple metal, for which the solvent-impurity-solvent triplet ion forces could be determined explicitly. The impurity-induced forces between host atoms near the solute hydrogen are found to be as strong as either the direct hydrogen-host-atom interaction or the host-host interaction in the pure metal; moreover, they have comparable large central and non-central (tangential) components. Angular analysis shows a strong isotropic component, as in a 'spherical solid' model, but the angular dependence is also important for host atoms with a small core radius. The relevance to lattice deformation and local force-constant changes at the defect is discussed.