Phase transition, elastic and thermodynamical properties of technetium monocarbide (TcC) in the WC, NiAs, NaCl, CsCl, and ZnS structures have been studied by full-potential linearized augmented-plane-wave (FP-LAPW) theory. From the enthalpy difference between the five structures, we predict that the structural phase transition from WC-type structure to CsCl-type structure occurs at ca. 411.4 GPa. Meanwhile, it is found that the NiAs, NaCl, and ZnS types are not stable phases in whole pressure ranges considered. In particular, for the first time we calculate the elastic properties and phase transition of TcC under high pressures. For WC TcC and CsCl TcC structures, the elastic constants, bulk modulus, shear modulus, and Young's modulus are predicted to increase monotonically with increasing pressure. The Vickers hardness of TcC under high pressure is estimated. The brittle-ductile behavior of TcC has been obtained by Pugh's criteria. Finally, the Debye temperature, isochoric heat capacity and thermal expansion coefficient are predicted by the quasiharmonic Debye model method.