A computational study of partial cavitation over axisymmetric bodies is presented using two numerical methods. The first method is based on the VOF technique where transient 2D Navier-Stokes equations are solved along with an equation to track the cavity interface. Next, the steady boundary element method (BEM) based on potential flow theory is presented. The results of the two methods for a disk cavitator are compared with each other and with those of the available experiments and analytical relations. The two methods are then used to predict the partial cavity over an axisymmetric body consisting of a disk cavitator followed by a conical section and ending in a cylindrical shape. The effects of various parameters such as cone length, cone angle, cavitator radius and cylinder diameter are investigated. The results show that as the cone length is increased, the cavity region covers a larger portion of the body. Reducing the cone angle increases both the length and diameter of the cavity region. For an axisymmetric body with a larger radius the cavity detachment is more likely to occur.