The density functional theory (DFT) with dispersion correction was used to study the tetravalent metal (Ti, Zr, Ge, Sn)-incorporated MTW-type (Mobil-TWelve) zeolites that are usually denoted as ZSM-12 (Zeolite Socony Mobil-twelve). Their stability, Lewis acidity, and structural properties were analyzed with periodic models. The calculated substitution energies indicate that Ti and Zr are more easily incorporated into MTW than Ge and Sn. The most stable substitution energies of four elements correlate with their covalent radii (R2 = 0.95), implying that the thermodynamics of incorporation process could be designed by covalent radii. Incorporations of a tetravalent metal result in the variation of cell volume due to their larger covalent radii; significantly, there is a good correlation between substitution energies and cell volume, indicating that the stability could be judged by the cell volume from accessible characterization. The Lewis acidity is measured by ammonia adsorption as follows: Sn-MTW > Zr-MTW > Ti-MTW > Ge-MTW. This finding provides the basis of theoretical Lewis acidity and agrees with previous experiments. In addition, the structural deformation has a great influence on the zeolitic stability, proved by two correlations: (1) relative mean square deviation of [MO4] and substitution energy of Ti-, Ge-, and Sn-MTW and (2) root-mean-square error of [MSi4] and substitution energy of Zr-MTW. Our work provides the theoretical basis for the preparation and Lewis acidity of tetravalent metal-incorporated MTW-type zeolitic catalysts.