The mechanical deformation of an ideal thin-walled cylindrical shell is investigated in the presence of intersurface interactions with a planar rigid substrate. A Dugdale–Barenblatt–Maugis (DBM) cohesive zone approximation is introduced to simulate the convoluted surface force potential. Without loss of generality, the repulsive component of the surface forces is approximated by a linear soft-repulsion, and the attractive component is described by two essential variables, namely, surface force range and magnitude, which are allowed to vary. The nonlinear problem is solved numerically to generate the pressure distribution within the contact, the deformed membrane profiles, and the adhesion-delamination mechanics, which are distinctly different from the classical solid cylinder adhesion models. The model has wide applications in cell adhesion and nanostructures.