Modelling floods and flood-related disasters has become priority for many researchers and practitioners. Currently, there are several options that can be used for modelling floods in urban areas and the present work attempts to investigate effectiveness of different model formulations in modelling supercritical and transcritical flow conditions. In our work, we use the following three methods for modelling one-dimensional (1D) flows: the MIKE 11 flow model, Kutija's method, and the Roe scheme. We use two methods for modelling two-dimensional (2D) flows: the MIKE21 flow model and a non-inertia 2D model. Apart from the MIKE11 and MIKE21 models, the code for all other models was developed and used for the purposes of the present work. The performance of the models was evaluated using hypothetical case studies with the intention of representing some configurations that can be found in urban floodplains. The present work does not go into the assessment of these models in modelling various topographical features that may be found on urban floodplains, but rather focuses on how they perform in simulating supercritical and transcritical flows. The overall findings are that the simplified models which ignore convective acceleration terms (CATs) in the momentum equations may be effectively used to model urban flood plains without a significant loss of accuracy.