We study plane shear waves in a continuum model for a saturated soil, assuming a hypoplastic flow rule. Following an earlier paper on velocity-controlled waves [1], we now specify a time-periodic stress disturbance on the boundary of a semi-infinite medium. As before, the stress saturates, tending at large times to a position-independent value, away from the boundary. By contrast, the dependence of this asymptotic state on the boundary data is strikingly different: in the previous case, this dependence was wildly discontinuous, while here it is very simple and smooth.