New 1111-like quaternary tetragonal Th-based phases: silicide arsenide ThCuSiAs and germanide arsenide ThCuGeAs are proposed in this article. The stabilities of these materials are verified, and the value of their structural, elastic (elastic constants, bulk, shear, and Young's moduli, compressibility, Pugh's indicator, Poisson's ratio, indexes of elastic anisotropy), electronic (densities of electronic states, electronic heat capacity, molar Pauli paramagnetic susceptibility, and the so-called metallicity indexes), and some other properties (Vickers hardness and melting temperatures) are predicted from the first principles calculations. The proposed phases are the first Th-based oxygen-free 1111-like materials, and their syntheses seem very attractive to expand the rather rare group of non-conventional quasi-three-dimensional 1111-like materials.