S OME pragmatic postulates of material behaviour, not given by thermodynamics, are reviewed critically. The postulates typically state lower bounds to the work expended on infinitesimal or finite paths of deformation. It is pointed out that such bounds implicitly depend on arbitrary choices of the strain measure. This dependence is investigated in the general context of conjugate stress and strain variables. Possible improvements to the inequalities are explored, having regard to the available evidence for actual materials. Part I is mainly concerned with elastic solids.