Abstract: Based on the theory of mathematical physics equation, thejoining conditions are proposed to establish the vibration equation oftrain-bridge (track) system. The joining conditions include the equilibriumcondition of contacting forces between wheel and rail and the displacementcondition. Only when the joining conditions are satisfied, the equation ofthe system is well-posed. The joining conditions are notsatisfied for the equation of the system currently in use.Train and bridge (track) are regarded as a whole system and the joiningconditions are formulated. With the principle of the total potential energy for formulating the system matrix equation, theequation of the system is founded which can make the system well-posed.