Summary: Effects of imposed pressure gradients on the solidification characteristics of planar Poiseuille-Couette flows are mathematically investigated. Under the assumptions of quasi-steady state heat transfer, closed form expressions are obtained for the variations in the dimensionless freeze-front location and the Nusselt number, as a function of the Brinkman number, Biot number and the dimensionless pressure gradient. It is revealed that an imposed pressure gradient effectively slows down the rate of interfacial growth, irrespective of whether the pressure gradient is favourable or adverse. Non-trivial influences of the pressure gradient on the instantaneous rate of interfacial growth are also noted.