Large forgings are crucial in aerospace applications; however, the residual stresses generated during their forming and heat treatment seriously affect their serviceability. Therefore, the non-destructive detection of residual stresses in large forgings is of far-reaching significance for ensuring the quality of forgings and realising precision machining. Although a variety of detection methods are available, there is still a lack of a programme that can comprehensively, accurately and non-destructively measure the residual stresses in large forgings. This study is dedicated to exploring the application of the bouncing impact indentation method in the non-destructive testing of residual stresses in large forgings. Through in-depth finite element simulations and orthogonal scheme analyses, we found that the elastic modulus, yield strength and work hardening indexes have significant effects on the impact indentation process. Further, we establish the dimensionless function of residual stress and indentation parameters, and successfully obtain the inversion algorithm of residual stress. The relative error of the calculated values of the indentation curves hm and hr in the simulation with reference values is not more than 3%, and the relative error of the corrected Pm inversion values for most virtual materials is not more than 5%. The folding elastic modulus and apparent elastic modulus obtained by inversion are controlled within 10%, which demonstrates a high value for engineering applications. In addition, we innovatively express the research results in the form of 3D stress diagrams, realising the digital expression of 3D residual stresses in large forgings based on feature point measurements and contour surface configurations, which provides intuitive and comprehensive data support for engineering practice.