Internally constrained mixtures of elastic continua

A treatment of internally constrained mixtures of elastic continua at a com mon temperature is developed. Internal constraints involving the deformatio n gradient tensors and the common mixture temperature are represented by a constraint manifold, and an internally constrained mixture of elastic conti nua is associated with each unique equivalence class of unconstrained mixtu res. The example of intrinsic incompressibility of each constituent first p roposed by Mills is discussed.