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The internal strain induced in a crystal structure by lattice deformation was considered. A suitable rotationally invariant representation was introduced and the corresponding contribution to the elastic constants was calculated. The method is based on the use of crystallographic rather than Cartesian atomic coordinates as variables of energy derivatives, with full exploitation of space-group symmetry and no constraint on the lattice geometry. A two-body Born interatomic potential was assumed, for both ionic and molecular crystals; energy derivatives of electrostatic lattice sums were calculated with the Ewald series. Molecular groups are treated within a rigid-body scheme based on Eulerian angles and translations as inner strain variables. Results of computations of Mg2SiO4 (forsterite) are reported, and the importance of optimizing the potential parameters against experimental data is discussed.