Four-dimensional Hooke's law can encompass linear elasticity and inertia

The question is examined, whether the formally straightforward extension of Hooke's time-honoured stress-strain relation to the four dimensions of spe cial and of general relativity can make physical sense. The four-dimensiona l Hooke law is found able to account for the inertia of matter; in the flat -space, slow-motion approximation the field equations for the "displacement " four-vector field Ei can encompass both linear elasticity and inertia. In this limit one just recovers the equations of motion of the classical theo ry of elasticity.