Highly filled suspensions (or pastes) present complex rheological behaviour and squeeze flow testing is used frequently for rheological characterisation. The extent to which liquid phase migration (LPM) occurs in such tests, and the influence of material extruded from between the plates, was investigated in experiments supported by detailed modelling based on soil mechanics approaches. Lubricated squeeze flow (LSF) tests were conducted on a model saturated ballotini paste prepared with a viscous Newtonian binder, at plate speeds spanning two decades. The tests were simulated using a two-dimensional (2 D) axisymmetric finite element model with adaptive remeshing to circumvent mesh distortion. The paste was modelled as a viscoplastic soil (Drucker-Prager) to capture both rate-dependent effects at high shear rates and LPM at low shear rates. Capillary pressure was applied at the evolving free surface and the plate surfaces were modelled as frictionless for simplicity. Reasonable agreement was obtained between the measured and predicted squeezing pressure profiles at the highest solids volume fraction tested (ϕs = 60%). Agreement was poor at the lowest ϕs (52.5%), which was due to this paste formulation behaving as a suspension/slurry without a distinct yield stress. For the first time, the predicted squeezing pressure was resolved into components using an energy analysis. The squeezing pressure was dominated by the work required to deform the paste in the gap. This result is specific to highly viscoplastic pastes and persisted to small plate separations when most of the sample lay outside the plates. Characterisation of the yield stress from the ‘shoulder’ in the squeezing pressure profile was reasonably accurate at h/h0 ≥ 96% (9% estimated error). LPM was neither observed nor predicted at the plate speeds tested, despite the favourable pore pressure driving force, due to the high binder viscosity and the zero dilation angle in the simulations. The flow field was characterised using a novel flow mode parameter derived from the shear rate tensor. The paste was predicted to undergo pure biaxial extension between the smooth plates, and for the first time was predicted to undergo pure uniaxial extension external to the plates and (briefly) pure shear at the boundary.