Compressed thin films deposited on substrates may buckle depending on the geometrical and mechanical properties of the film/substrate set. Until recently, the small dimensions of the buckling have prevented measurements of their local in plane internal stress distribution. Using a scanning x-ray microdiffraction technique developed at a third generation x-ray synchrotron source, we obtained thin film internal stress maps for circular blisters and telephone chord buckling with micrometric spatial resolution. A fair agreement was found between the film delamination topology observed by optical microscopy and the measured stress maps. We evidenced residual stress relaxation associated with the film buckling: the top is essentially stress free while adherent region exhibits large compressive stresses.