The mechanical properties of several types of block copolymer (BCP) thin films have been investigated using PeakForce quantitative nanomechanical mapping. The samples consisted of polystyrene/poly(methylmethacrylate) (PS/PMMA)-based BCP thin films with different pitches both randomly oriented and self-assembled. The measured films have a critical thickness below 50 nm and present features to be resolved of less than 22 nm. Beyond measuring and discriminate surface elastic modulus and adhesion forces of the different phases, we tuned the peak force parameters in order to reliably image those samples, avoiding plastic deformation. The method is able to detect the changes in mechanical response associated with the orientation of the PMMA cylinders with respect to the substrate (parallel versus vertical). The nanomechanical investigation is also capable of recognizing local stiffening due to the preferential growth of alumina deposited by atomic layer deposition on BCP samples, opening up new possibilities in the field of hard mask materials characterization.