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In this study, tantalum carbide (TaC) samples were placed in a diamond anvil cell to study the equation of state at room temperature and high pressure using synchrotron radiation X-ray diffraction. By fitting the data at ambient pressure and up to the highest pressure of 38.5GPa, we obtained the bulk modulus and first derivative of TaC as $K_0=290.7$ (6.8) GPa and $K_0^{\prime }=3.05$ (0.49), respectively. In addition, we calculated the bulk modulus and band structure of TaC under high pressure using density functional theory. The obtained bulk modulus is 267 (3)GPa. TaC is metallic in nature throughout the entire pressure range. We studied the high-pressure deviatoric stress of TaC using linewidth analysis method. We found that TaC can support a maximum differential stress of up to 18.6GPa at the highest pressure of 38.5GPa.