The ternary copper-based chalcogenides Cu(3)TMCh(4) (TM = Cr, Fe and Ch = S, Se, Te), which have simple cubic (SC) crystal structure and conform to space group with 215 space number, have been investigated by spin-polarised generalised gradient approximation (GGA) in the framework of density functional theory (DFT). All systems have been considered in ferromagnetic (FM) order. The mechanical and thermal properties and the electronic band structures of these systems have been investigated after the well-optimised structural parameters have been obtained. The spin-polarised electronic band structures of all the systems exhibit half-metallic behaviour with band gaps in minority spin channel from 0.29 eV for Cu3FeTe4 to 1.08 eV for Cu3CrS4, while metallic band structures are observed for majority spins. This agrees with the calculated total magnetic moments which are close to integer values. The calculated negative formation enthalpies indicate the energetic and thermodynamic stability of these compounds. Moreover, the calculated elastic constants verify that these materials are stable mechanically due to satisfying Born stability criteria. The estimated anisotropy shear factors show that Cu3FeS4, Cu3FeSe4 and Cu3CrSe4 systems have nearly isotropic character with 1.004, 0.910, and 0.958 values, respectively, whereas other compounds have relatively low anisotropic behaviour.