Simultaneous fits of the Kaye‐BKZ and Wagner equations to shear and uniaxial extensional flow data are not the most critical tests of these equations, because their memory functions depend on two strain invariants, and this dependence can be varied independently for shear and for uniaxial extension to obtain a fit for each. In planar deformations, however, the memory function depends on only one invariant; this dependence can be measured in single‐step shear experiments, as is reported here for a branched polyethylene, IUPAC X, using a sliding plate rheometer. Predictions are then made for three different planar deformation histories: start‐up of steady simple shear and steady planar extension, and exponentially growing shear, all tests in which the memory function depends on only one invariant. The predictions in steady shear and exponential shear are in rough agreement with the data. The theory for planar extension, however, greatly underpredicts the experimental strain hardening of IUPAC X, which has been reported to be similar to the strain hardening usually seen in uniaxial extension for LDPE. Thus, the Kaye‐BKZ and Wagner single‐integral equations cannot simultaneously describe both strain softening in shear and extreme strain hardening in planar extension using a damping function obtained from one of these flows.