The first use of the asymptotic approach to investigate two-dimensional plane strain rolling was performed by Smet and Johnson [1]. In this paper we investigate scalings useful for examining plane strain rolling when the friction causes the roll pressure to significantly exceed the flow stress. Two cases are studied. In the first the reduction is small while in the second the reduction is large. The Taylor series expansion of the boundary conditions at the roll-material interface simplifies the generation of the asymptotic approximations for the first case. The example chosen for the second case corresponds to that chosen by Smet and Johnson [1]. Using the scalings introduced in this paper it is possible to significantly simplify their analysis. The resulting asymptotic approximations provide estimates of the inhomogeneous effects for both cases.NOTATIONB work hardening coefficienth incoming strip half thicknessk yield stress in shearl p length of plastic region in roll gapn work hardening coefficientp hydrostatic pressurep m maximum roll pressurer dimensionless reductions roll pressures x frictional force at roll material interfaceS u deviatoric stresst timet s tension force per unit widthv i velocity componentV 0 incoming strip velocityx, y co-ordinatesY flow stressδ ηrΔh material half reduction effective plastic strainη h 0 l p λ plastic flow multiplierμ coefficient of frictionσ i i stress componentσ 0 annealed yield stressτ kp m dimensional quantity(i) order of approximation