I t is shown that remarkable connexions exist between solutions to certain superficially dissimilar boundary-value problems in plane strain of an elastic solid. Essentially, these connexions relate the displacement at a point in either state to the force resultant on a curve to the point in the other; as a consequence, related states can be recognized from their defining boundary-conditions alone: Many examples are given, including several problems not hitherto solved. Analogous results in steady quasi-static viscous flow are discussed. These complement and complete the correspondences noted by G oodier (1934) between plane states of deformation in an elastic solid and a viscous fluid.