Theoretical developments on cavity flow studies are briefly reviewed. Physical and mathematical difficulties involved in cavity flow problems are discussed. Particular attention, with regard to practical applications, is given to the development of linearized theories. Based on the existing analyses, efforts to develop simple approximate expressions for the force coefficients of supercavitating hydrofoils (including the effects of free surface, cascade, aspect ratio, and finite disturbance) are made. Numerical results calculated from these expressions are compared with existing experimental data. Special problems involving unsteady cavity flows, such as pulsation of the finite cavities, are also discussed.