The local residual stresses in microzones are investigated by the instrumented indentation method with the Berkovich indenter. The parameters required for determination of residual stresses are obtained from indentation load–penetration depth curves constructed during instrumented indentation tests on flat square 7050-T7452 aluminum alloy specimens with a central hole containing the compressive residual stresses generated by the cold extrusion process. The force balance system with account of the tensile and compressive residual stresses is used to explain the phenomenon of different contact areas produced by the same indentation load. The effect of strain-hardening exponent on the residual stress is tuned-off by application of the representative stress $$\sigma_{0.033}$$ in the average contact pressure assessment using the $$\varPi$$ theorem, while the yield stress value is obtained from the constitutive function. Finally, the residual stresses are calculated according to the proposed equations of the force balance system, and their feasibility is corroborated by the XRD measurements.