Bores generated by dam-break and initial mound of water and their propagation over horizontal and inclined surfaces are studied by use of theoretical approaches. Calculations are carried out in two and three dimensions and particular attention is given to the bore impact on horizontal and vertical surfaces. Downstream of the initial mound of water may be wet or dry. Discussion is provided on the influence of the downstream water on the bore behaviour and impact. Three methods are used in this study, namely the Reynolds-Averaged Navier-Stokes equations (RANS), the Green-Naghdi (GN) equations and Saint Venant equations (SV). The governing equations subject to appropriate boundary conditions are solved with various numerical techniques. Results of these models are compared with each other, and with laboratory experiments when available. Discussion is given on the limitations and applicability of these models to study the bore generation, propagation and pressure on horizontal and vertical surfaces. It is found that the GN equations compare well with the RANS equations, while the SV equations have substantially simplified the solution.