The dead load traction boundary condition in finite elasticity is the prescription of the first Piola-Kirchhoff stress vector on the boundary of the undeformed body. Such a prescription does not correspond to an unambiguous physical situation: more than one pair of deformation and actual applied traction on the deformed body can produce the same Piola-Kirchhoff stress vector on the undeformed body. The ambiguous physical meaning of the assignment of the Piola-Kirchhoff traction makes it essential that each solution to a dead load boundary value problem be interpreted in terms of the deformed configuration of the body and the Cauchy traction on the deformed boundary in order to determine the physical situation to which it corresponds. The purpose of this paper is to illustrate the important role played by physical interpretation of solutions through the examination of two familiar problems of dead loading: the biaxial stretching of a sheet of rubber material, studied by Treloar; and the problem, introduced by Rivlin, of a neo-Hookean cube loaded by three equal pairs of forces. In each of these dead load problems the loads are equal but produce multiple deformations most of which are asymmetric. This feature has been thought surprising by a number of authors. Here it is shown that the occurrence of these multiple solutions does not appear unusual when the solutions are interpreted in terms of the physically meaningful Cauchy tractions on the deformed body.