The response of an infinite beam on an elastic foundation depends on the property/modeling of the foundation. There is a qualitative difference between the responses of a beam when it is on the Winkler foundation and on the tensionless foundation. A bilinear elastic foundation model, which describes the different behaviors of the elastic foundation in the tensile and compressive zones with two different foundation moduli, is proposed and a straightforward computational method is also formulated. The Winkler and tensionless foundations are shown to be the two special cases of the bilinear elastic foundation model. With this bilinear elastic foundation model, a more general method of modeling an elastic foundation is provided, which can be of some help to the modeling of the support of the ballastless high-speed railway.