The paper presents the theoretical estimation of Additional Finite Element Method (AFEM) from the point of view of the Numerical Method Theory. AFEM is the variant of Finite Element Method (FEM). This variant extends FEM abilities for analysis of N-nonlinear systems under the growth of applied load and the number of physical nonlinear properties. Mathematical modeling process realizes by introduction of additional finite elements (AFE-s) into additional design diagrams (ADD-s). This helps the gradual transformation of main set of equations at every step of analysis. The last step is the limit state moment of considered system, when their design diagram transmits into ideal failure model (IFM).