This thesis deals with the theory and the numerical simulation of sheet cavity flows on arbitrary lifting bodies like hydrofoils and propeller blades. The objective of this research is the accurate prediction of the cavity volume and the volume variations in time when these lifting bodies travel in a gust or are subject to an ambient pressure change. This volume change plays an important role in the pressure excitation on neighbouring structures like hull of a ship and in the radiation of underwater noise. The physical phenomenon of sheet cavitation on lifting bodies is described according to experimental observations at the beginning of this thesis. The specific features of sheet cavitation, different from bubble and cloud cavitation, are addressed. The basic cavity flow theory within the frame of the potential theory is described and all the boundary conditions are discussed in order to obtain the solution of the problem. For predicting the dynamics of the cavity, numerical methods to find the solution in time are studied. All the numerical algorithms for solving the problem are discussed in detail and checked extensively by numerical tests. A higher order panel method is described and evaluated. Emphasis is given to the problems of the analytical calculation of the influence coefficients. The system of equations of the fully wetted and cavitated flows are established under different Kutta conditions. The detachment condition and its influence on the cavity flow are studied. Cavity planform searching, grid updating and cavity-body intersection are described. Other highly-related numerical methods for panel methods and cavity flows, like the Kutta condition and wake alignment, are investigated and checked by numerical tests. Specific attention is paid to the influence of these numerical algorithms on the calculated results. The present method for predicting steady sheet cavity flows on two-dimensional and three-dimensional hydrofoils and on propeller blades is used extensively and validated by experimental results in this thesis. Good agreement between the calculations and the experiments is achieved. The dynamics of sheet cavitation is predicted by the present method for a hydrofoil moving into a sinusoidal gust and for a propeller rotating in a sharp wake peak. The present method demonstrates the ability of capturing the dynamic movement of the sheet cavitation. At the end of the thesis, the conclusion is drawn that the present method has the potential to predict the cavity topology and the cavity dynamics. After improvement of some numerical algorithms, the efficiency of the method can be enhanced to such a level that it can be applied in the early stage of ship propeller design in order to prevent excessive cavitation and vibrations.