Received experimental data about a rivet tear-out force size with a flat head from polymeric composite materials samples. Investigated their stress state using finite element method. Suggested the deformation criteria to determination of force value required to tear out the rivet head from the composite material skin on the base of comparison the calculated results with experimental data. Using the proposed criteria the experimental values area of interlaminar stresses arising due to tearing out the river head from composite material is expanded.