Contact mechanics in wrapping a thin-shell (tape/web) around a grooved cylindrical surface (roller) under tension is investigated. The problem is analyzed along the axial direction of the roller, and the effects of wrap-angle tape/web motion are neglected. Equations of equilibrium admit analytical solutions, but the problem is nonlinear due to the unknown nature of contact area. The tape bends into the grooves and makes contact over the lands. Three distinct contact states describe the interaction of the tape/web with respect to the lands. Nondimensional analysis shows that contact state depends on the width of the groove and the land, and the nondimensional belt-wrap pressure only modulates the amplitude of the deflected profile.