When a viscous fluid spreads underneath a deformable surface skin or crust, the peeling dynamics at the fluid front can control the rate of advance rather than bulk self-similar flow. For an elastic skin, this control results in a quasi-static interior blister held at constant pressure that is matched to a narrow peeling region behind the fluid front. In this paper, the analogous problem is considered for a skin that deforms either viscously or plastically, or both. In particular, the deformable surface is assumed to be a thin plate of material governed by the Herschel-Bulkley constitutive law. We examine how such a skin controls viscous flow underneath, fed at constant flux and spreading as either a planar or axisymmetric current. As for an elastic skin, the peeling dynamics at the viscous fluid front again controls the rate of spreading. However, contrary to that situation, the mathematical matching problem for viscoplastic peeling is simplified considerably as a result of an integral constraint. Despite this, the structure of the peeling region is complicated significantly by any plasticity in the skin, which can create a convoluted peeling wave ahead of the main blister that features interwoven yielded and plugged sections of the plate.
