In this paper different approaches aimed at investigating the dynamic behaviour of circular tunnels in the transverse direction are presented. The analysed cases refer to a shallow tunnel built in an ideal soft clayey deposit excited by four different acceleration time histories characterised by significantly different frequency content. The adopted approaches include: 1) one-dimensional (1D) numerical analyses performed modelling the soil as a single phase visco-elastic non-linear medium, the results of which are then used to evaluate the input data for selected analytical solutions proposed in the literature (uncoupled approach); 2) 2D fully coupled Finite Element simulations adopting visco-elastic and visco-elasto-plastic constitutive assumptions for the soil and the lining (coupled approach); 3) 2D quasi-static Finite Element simulations adopting the same constitutive hypotheses of the fully coupled dynamic analyses. The three approaches, when a proper calibration of the soil parameters is undertaken, provide comparable results in the case of the visco-elastic assumption for the soil. The different constitutive hypotheses adopted in the 2D Finite Element simulations prove to play a significant role on the seismic-induced loads and curvature of the lining.