The main goal of this paper is to introduce a novel method that allows us to construct systematically models of mereology. We call the resulting method mereological forcing. Whereas set-theoretic forcing deals with the construction of models which witness the compatibility of ZFC with certain set-theoretic statements, mereological forcing, is about the construction of models that establish the compatibility of a given mereological theory with certain mereological statements. Consequently, we claim that such a method constitutes a powerful tool for establishing compatibility claims for the mereologist. More concretely, we showcase this by constructing models which display the compatibility of (atomic) classical mereology with the mereological statement that expresses that their exist inconsistent objects.