Research conclusions: The finite element method was used to set up a longitudinal integration calculation model of rail －track slab － bridge － pier based on the longitudinal interaction mechanism of line － bridge － pier，and the corresponding general calculation program was compiled． With the program，the longitudinal stresses behaviour of the commonly － used 5 × 32 m simply － supported beam bridge and continuous bridge of passenger dedicated line were calculated，and the analyses of the parameter influence of the fastener longitudinal resistance，resin elastic modulus of the convex plate， friction coefficient of the bottom track slab and the temperature load value were made． The calculation results show ( 1) For the long grade slab track，the longitudinal relative displacements of rail － slab and slab － bridge should be limited within the range of 0． 2 mm and the corresponding resin elastic modulus of convex plate should be larger than 120 MPa． ( 2) The brake effect and longitudinal component force of live load should be applied to the bridge on long grade to make the computational check of convex plate． At the same time，the convex plate structure should be strengthened and the bonding strengths of convex plate，filling resin and track slab should be enhanced．