Recently, the non-centrosymmetric WC-type materials (i.e., MoP, ZrTe, TaN, etc) have attracted extensive interest due to the discovery of their topological properties. By means of the first-principles calculations, here we have investigated the structural, thermodynamic, elastic, and electronic properties of the WC-type MX compounds (TiS, TiSe, TiTe, ZrS, ZrSe, ZrTe, HfS, HfSe, and HfTe). Among these nine compounds, five of them (TiS, ZrS, ZrSe0.9, ZrTe, and Hf0.92Se) have been experimentally synthesized to crystallize in the WC-type structure and other four members have never been reported. Our calculations demonstrated that they are all structurally, thermodynamically, and dynamically stable, indicating that all of them should be possibly synthesized. We have also derived their elastic constants of single crystalline and their bulk and shear moduli in terms of the R. Hill approximations. Furthermore, in similarity to ZrTe, all these compounds have been theoretically derived to be topological semimetals. Whereas TiS is unique because of the coexistence of the Dirac nodal lines (DNLs) and sixfold degenerate nodal points (sixfold DNPs), the other eight members are revealed to exhibit coexisted Weyl nodes (WPs) and triply degenerate nodal points (TDNPs). Their electronic and topological properties have been further discussed.