The groups of equivalence transformations for a family of second order balance equations involving arbitrary number of independent and dependent variables are investigated. Equivalence groups are much more general than symmetry groups in the sense that they map equations containing arbitrary functions or parameters onto equations of the same structure but with different functions or parameters. Our approach to attack this problem is based on exterior calculus. The analysis is reduced to determine isovector fields of an ideal of the exterior algebra over an appropriate differentiable manifold dictated by the structure of the differential equations. The isovector fields induce point transformations, which are none other than the desired equivalence transformations, via their orbits which leave that particular ideal invariant. The general scheme is applied to a one-dimensional nonlinear wave equation and hyperelasticity. It is shown that symmetry transformations can be deduced directly from equivalence transformations. (C) 1999 Elsevier Science Ltd. All rights reserved.