As polymers are deformed anisotropically in the rubbery state, the molecules tend to become oriented there and retain varying degrees of that orientation as they are cooled into the glassy state. This frozen‐in orientation, which occurs in practically all polymer processes (intentionally or otherwise), can have significant effects on the subsequent glassy properties; also, of course, some changes may take place over time (orientation aging). While the physics of the induction and subsequent release of molecular orientation is clear enough qualitatively, we have lacked a quantitative formulation. Present viscoelastic theory is capable of “remembering” prior deformations, but little or nothing has been done with it as one passes through the glass transition. We carry out such an analysis here, dealing with both the rubbery deformation and the subsequent glassy shrinkage (or creep, if loaded) in a single theoretical formulation. A generalization of viscoelastic theory to include volume (compressible) effects is made in the following article; here we operate in the framework of existing theory, in which incompressibility is assumed.