In this paper, we present a formulation for coupling discrete and continuum models for both dynamic and static analyses. This kind of formulation offers the possibility of carrying out better simulations of material properties than the discrete calculations, and with both larger length scales and longer times. Using only a discrete approach to simulate a large medium composed of many degrees of freedom seems very difficult in terms of calculation and implementation. Moreover, using only a continuum approach does not give an accurate solution in a zone where particular and localized phenomena can occur. A direct application of our coupling approach to the case of railway track models subjected to an external load, is proposed for its validation.