[en] The addition of interstitial atoms to a metal lattice has been likened to the addition of extra billiard balls to an array of tangentially touching billiard balls. In such a picture the increased clustering of interstitials can lead to the buildup of larger and larger strain fields which ultimately are associated with the production of broken bonds. Simple models of the strain fields associated with the addition of particles to a lattice in which the force exerted between the added atoms and host atoms is finite have been studied. From these studies one can define situations in which the billiard-ball approach has qualitative validity and those in which it is inappropriate. Basically, those situations in which the displacements of the host atoms can be represented as involving acoustic phonons yield long-range strain fields analogous to those of the billiard-ball model with the radius of the extra billiard ball being determined by the stiffness of the host lattice and the forces between the added atom and the surrounding host atoms. If the displacements produced by the added atoms are represented as involving primarily optical phonons the displacement pattern is short-ranged and not described by the usual elasticity theory. For example, Vegard's law does not apply in these instances. Such concerns arise in considering the strains induced by interstitial helium in tritides