This paper describes the construction of a stochastic model of urban railway track geometry irregularities, based on experimental data. The considered irregularities are track gauge, su-perelevation, horizontal and vertical curvatures. They are modelled as random fields whose statistical properties are extracted from a large set of on-track measurements of the geometry of an urban railway network. About 300 to 1000 terms are used in the Karhunen-Lò eve/Polynomial Chaos expansions to represent the random fields with appropriate accuracy. The construction of the random fields is then validated by comparing on-track measurements of the contact forces and numerical dynamics simulations for different operational conditions (train velocity and car load) and horizontal layouts (alignment, curve). The dynamics simulations are performed both with and without randomly generated geometrical irregularities for the track. The power spectrum densities obtained from the dynamics simulations with the model of geometrical irregularities compare extremely well with those obtained from the experimental contact forces. Without irregularities, the spectrum is 10 to 50 dB too low.