An analytical model is developed to calculate the dynamic response of a cracked multi-span continuous beam, subjected to a multiple-axle vehicle load. In this model, the vehicle load is considered as a series of concentrated moving loads at a constant velocity. Meanwhile, the crack is modelled by a spiral spring. Thereafter, the cracked span is considered as a two-span beam, connected by the spring at the position of the crack. By using the Euler-Bernoulli beam theory, the relations between the two successive spans can be obtained from the boundary conditions at the supports and the position of the crack. This technique makes it possible to calculate the eigenmodes of the beam. The response of the beam is finally obtained by the superposition of the modes. This model allows us to quickly analyze the influence of the cracks (depth, location) and of the vehicle (loads, velocity) on the response. Moreover, this model is validated by finite element modelling and some numerical results are given.