We investigate the contact of a cylindrical punch with an adhesive elastic layer or film bonded to a rigid substrate. The classical assumption of Hertzian contact are coupled with tools of fracture mechanics to resolve the contact problem. The contact edge's singularity is resolved by introducing a Dugdale-Barenblatt model for the adhesive zone extending in front of the contact region. Exact governing equations so obtained are solved by a semi-analytical technique employing Chebyshev polynomials. We also extend the useful JKR approximation to the indentation of elastic layers as a particular case of our general solution. © 2012 Copyright Taylor and Francis Group, LLC.