We present a constitutive equation that describes the nonlinear elastic response of aqueous foams and concentrated emulsions that undergo affine deformations. We derive it from the expression for interfacial energy of strained aqueous foam or concentrated emulsions using the formalism of large deformation continuum mechanics. By linearizing the strain energy potential, we obtain a constitutive equation of Mooney-Rivlin form. The predicted nonlinear elastic response is compared to that in previous models and numerical simulations. Furthermore, we discuss the approximations used, particularly those regarding the nonaffine character of deformation in real foams and concentrated emulsions. (C) 2004 The Society of Rheology.