We analyze the existing models of granular flow where the particle’s phase stress tensor is regarded as dominated by translational‐collisional stresses. We extend the commonly used concept of a granular phase pseudo‐temperature to develop a pseudo‐thermodynamic theory of such systems. This is accomplished by introducing the concept of pseudo‐entropy, a quantity which can actually be calculated from the existing theories. The systems considered are shown to exhibit entropic elasticity. The consistency of constitutive equations available in the literature is tested against the pseudo‐thermodynamic theory; the test is mostly successful, except for one term sometimes used in the constitutive equation for the flux of pseudo‐energy, which, according to our theory, should be identically zero.