A finite element method is used to calculate stresses and strain rates in a thin viscous sheet, representing the continental lithosphere, that is bordered in one part by an indenting boundary. We calculate solutions for velocity fields, crustal thickness distributions, strain rates, rotation (time-integrated vorticity), and finite strain ellipsoids to show the dependence of these quantities on the controlling parameters: the stress-strain exponent n and the strength of the sheet relative to the gravitational forces (which may be expressed as a dimensionless number: the Argand number Ar). For n>3 and Ar between 1 and 10 a plateau of thickened crust is formed in front of the indenter. The strain histories of individual elements within the viscous sheet may be quite complex, and the finite strain at the end of deformation may bear no obvious relation to the principal stress orientations during the deformation. The strain rate fields are interpreted in terms of the style of faulting that would be expected in the brittle upper crust if it were coupled to the ductile, but stronger, upper mantle. In general, the length scale of deformation increases with Ar and time since the start of the collision and decreases with n; for Ar>3, the increase in length scale is accompanied by a change in the style of deformation: from predominantly crustal thickening (with thrust faulting in the brittle layer) to predominantly transcurrent deformation (strike-slip faulting in the brittle layer).