The shear response of polymer brushes is explored as a function of grafting surface curvature using the Alexander-deGennes ansatz, where the free ends of the chains are localized at the tip of the brush and all tethered chains in the brush are stretched equally. Brushes adsorbed onto the concave and convex surfaces of a cylinder are found to swell to a maximum of 35% of their nonsheared brush height in good solvent, larger than the predicted maximum shear swelling of planar brushes of the same grafting density. For significantly convex surfaces, increased surface curvature increases the maximum amount of shear swelling. In contrast, brushes grafted onto concave surfaces with the same grafting density show diminished shear swelling as the grafting surface becomes more concave. The shear response of nonplanar brushes is important in a variety of possible applications, including the fabrication of pressure-sensitive microvalves and dynamic membranes and an understanding of the rheological behavior of hairy-rod polymers or molecular bottlebrushes.