A French project named REVES started in 2015. The goal of this project is to design ballastless railway tracks without sleepers in order to reduce track thickness and increase gauge in tunnels. Older tunnels would benefit particularly from such a track since it would allow for modern freight trains to circulate inside them while providing a cost-effective and time-saving construction process. A PhD thesis has begun within this project. It aims at modelling the viscoplastic behaviour of asphalt concretes in order to predict the long-term mechanical response of a railway infrastructure such as those considered in project REVES. A viscoplastic model using the Perzyna formulation was developed to describe the irreversible creep behaviour of asphalt concretes. Model parameters were identified by means of triaxial tests. An efficient yield surface was developed as well as a hardening law with a single parameter. A sequential method for determining model parameters was established. The model was implemented in FEM software Cast3M in order to perform numerical railway track simulation. Some simulations of ballastless railway structures were performed. Firstly, it can be observed than predicted settlements stabilizes and do not reach the limits recommended by the French railway board. It can also be seen that viscoplastic strains concentrates in the Asphalt concrete, just under the rail. Then, it can be seen that stresses redistribute inside the structure over time, leading to eliminate tensile and shear stresses.