Many problems involve the spreading of a viscous fluid underneath a surface skin or crust, such as the intrusion of magma into the crust, the formation of ordered wrinkle patterns to produce microfluidic devices, and the reopening of airways in biological fluid mechanics. A characteristic of these types of problems is that the spreading is controlled by the physics at the fluid front rather than a bulk similarity solution. This leads to a matching problem between an interior blister and the behaviour of the peeling region at the front. In this talk, I will consider the spreading of a viscous fluid underneath a viscoplastic plate with a Herschel-Bulkley rheology. This problem gives rise to a range interesting similarities and differences with the more classically studied flow underneath an elastic plate.