An Euler solver based on artificial-compressibility and pseudo-time stepping is developed for the analysis of partial sheet cavitation in two-dimensional cascades and on isolated airfoils. The computational domain is adapted to the evolution of the cavity surface and the boundary conditions are implemented on the cavity interface. This approach enables the cavitation pressure condition to be incorporated directly without requiring the specification of the cavity length or the location of the inception point. Numerical solutions are presented for a number of two-dimensional cavity flow problems, including both leading edge cavitation and the more difficult mid-chord cavitation condition. Validation is accomplished by comparing with experimental measurements and nonlinear panel solutions from potential flow theory. The demonstrated success of the Euler cavitation procedure implies that it can be incorporated in existing incompressible CFD codes to provide engineering predictions of cavitation. In addition, the flexibility of the Euler formulation may allow extension to more complex problems such as viscous flows, time-dependent flows and three-dimensional flows.