Two different consistency criteria are considered for the stress tensor expressions of two different kinetic theory models for dilute polymer solutions. The criteria are material objectivity and thermodynamic consistency. Two separate approaches for checking thermodynamic consistency are considered, the first proposed by Grmela [Phys. Lett.111A, 41 (1985)] and the second by Jongschaap [LectureNotesinPhysics(Springer, Berlin, 1991)]. The two models considered are a Hookean dumbbell model with internal viscosity (no linearization or rotation matrix approximations), and an inertial, elastic bead‐spring chain. Both sets of criteria may be applied to these models without finding either a closed‐form expression for the stress tensor, or solving any of the equations. We find that the Giesekus form for the stress tensor expression for a Hookean dumbbell with internal viscosity is both thermodynamically consistent and objective, whereas the Kramers form is not thermodynamically consistent. The Kramers form for the stress tensor is found to be thermodynamically consistent for an inertial, elastic bead‐spring chain, but is not materially objective. We also find that the approaches of Grmela and Jongschaap are the same, although each requires a differentansatzfor the relationship between thermodynamic quantities and polymer conformations.