In this paper, the influence of modeling the fastening with solid railpads on the vertical dynamics of railway tracks with monoblock sleepers is investigated. A 3D finite element (FE) model is presented with four different fastening representations: (1) commonly used spring-damper pair, (2) area covering spring-damper pairs, (3) solid railpad connected to the rail, and (4) solid railpad in frictional contact with the rail and fixed to the support by preloaded springs, which represent the clamps. The response of the four models to hammer excitation is simulated in the time domain, and the calculated response is transformed into the frequency domain to analyze how the models capture the seven main characteristics of tracks with monoblock sleepers. The numerical results show that the model with solid railpads and clamps reproduce the seven characteristics at a maximum frequency difference of 6%, while the conventional model with spring-damper pairs reaches only a 27%. In the improvement of the fit from multiple spring-damper railpad models to solid railpad models, the two key aspects identified are the Poisson's effect and the damping of the ballast. Additionally, the railpad type investigated showed a frequency-independent behavior, at least with acceptable error. In view of the close fit, the models with solid railpads can be used for track and fastening design and to derive track parameters to, for instance, study the deterioration of tracks. (C) 2014 Elsevier Ltd. All rights reserved.