We consider a conformal contact problem between a rubber band and rigid cylinders that involves geometrical and material nonlinearities. The rubber band is assumed to be incompressible, neo-Hookean rubber. From the geometry and elasticity of the band, we present simple formulas to estimate the force–stretch relations and the contact pressure distributions on the cylinder. We show that the theoretical results are in good agreement with those of the finite element analysis when the rubber band is thin enough to be negligible to the bending stiffness. This verifies that the theory can effectively take into account both the material and geometrical nonlinearities of the band under the present conditions.