In this paper, the performance of three different numerical approaches in cavitation modelling are compared by studying two benchmark test cases to understand the capabilities and limitations of each method. Two of the methods are the well established compressible thermodynamic equilibrium mixture model and the incompressible transport equation finite mass transfer mixture model, which are compared with a third method, a recently developed Lagrangian discrete bubble model. In the Lagrangian model, the continuum flow field is treated similar to the finite mass transfer approach, however the cavities are represented by individual bubbles. Further, for the Lagrangian model, different ways to consider how the fluid pressure influences bubble dynamics are studied, including a novel way by considering the local pressure effect in the Rayleigh-Plesset equation. The first case studied is the Rayleigh collapse of a single bubble, which helps to understand each model behaviour in capturing the cavity interface and the surrounding pressure variations. The special differences between the Lagrangian and finite mass transfer models in this case clarify some possible origin for some limitations of the latter method. The second investigated case is the collapse of a cluster of bubbles, where the collapse of each bubble is affected by the dynamics of surrounding bubbles. This case confirms the importance of considering local pressure in the improved form of the Rayleigh-Plesset equation and illustrates the influence of the liquid compressibility for cavity modelling and appropriate capturing of the collapse pressure. (C) 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license.