Attempts are being made to predict multicomponent azeotropic mixtures from the physical property of pure component and compositions of the constituting binary combination pairs. A modified response surface methodology(MRSM) model has been proposed with correlates boiling temperatures of binary, ternary and quaternary mixtures directly with the compositions of vapor and liquid phases. The generalized MRSM-2 models for liquid and vapor phases are proposed as follows: _{N N-1N N-1N N-1N} T = Σ T_iX_i + ΣΣA_ij X_iX_i +ΣΣB_ij X_iX_i(X_i-X_j) + ΣΣC_ij X_iX_i(X_i-X_j)² (for liquid phase) ^{I=1 i≠j i≠j i≠j} _{N N-1N N-1N N-1N} T = Σ T_iY_i + ΣΣA_ij Y_iYj +ΣΣB_ij Y_iYj(Y_i-Y_j) + ΣΣC_ij Y_iY_i(Y_i-Y_j)² (for vapor phase) ^{I=1 i≠j i≠j i≠j} These models require normal boiling point of the pure components, T_i and group-group parameters A_ij B_ij & C_ij which can be estimated by the group-group concepts of the constituent components. Therefore, this methodology is applied for the system of three and four components by the computer simulation. No experimental data is required is applied for the system of three and four components by the computer simulation. No experimental data is required for seeking of composition and temperature of the multicomponent azeotropic mixtures. By means of this methodology, MRSM, it is possible to depict an isothermal line map, temperature contours of the individual phase of the constituting ternaries for each quaternary system. Furthermore, it is possible to predict the azeotropic behaviors, maximum, minimum, saddle or any other type of azeotropic mixtures by examining the graphic contours obtained by computer graphics in the triangular coordinate for ternary and tetrahedron for quaternary. The proposed methodology (MRSM model) has been tested and compared successfully with previously reported azeotropic data in various journals for several ternary and quaternary multicomponent systems. Two azeotropic mixtures are newly found for each of two different quaternary tetrahedrons. The composition, temperature and type of the newly found azeotropes are reported.