Gravity models of the constrained, unconstrained and elastically constrained type are interpreted as reduced forms of spatial price equilibria of interregional trade. The explicit forms of equilibrium models reducing to the different varieties of gravity models are presented. They are theoretically consistent in the sense that the underlying demand and supply functions are compatible with individual optimising behaviour. Forms other than the gravity type, however, are consistent as well. No choice can be made by mere theoretical arguments. But additional criteria like computational facility and factual conformity provide good reasons for preferring gravity forms in applied work.