We consider shear flows that comprise of step changes in the shear rate. For these flows, we derive analytic solutions of the Rolie-Poly constitutive equation. Our method involves piecing together solutions for constant rate shear in a variety of flow rate regimes. We obtain solutions for interrupted shear, recoverable strain and nonlinear relaxation following cessation of flow. Whenever strong flow is present we neglect reptation, as other mechanisms dominate and for interrupted shear our solution is approximate as we neglect convective constraint release (CCR). Our analytic solutions provide new insight in several ways. These include revealing the mechanism of some experimental features of these flows; suggesting a method to extract the polymer contribution to the normal stress in the velocity gradient direction (sigma(yy)) from shear stress measurements alone; and a method to isolate the influence of CCR from damping function measurements. We also run complementary Graham, Likhtman and Milner, McLeish (GLaMM) model calculations to verify that insight from our analytic approach translates to this more detailed model. (c) 2017 The Society of Rheology.