A fixed-length Boundary Element Method (BEM) is used to investigate the super- and partial cavitating flows around various axisymmetric bodies using simple and reentrant jet models at the closure zone of cavity. Also, a simple algorithm is proposed to model the quasi-3D cavitating flows over elliptical-head bodies using the axisymmetric method. Cavity and reentrant jet lengths are the inputs of the problem and the cavity shape and cavitation number are some of the outputs of this simulation. A numerical modeling based on Navier-Stokes equations using commercial CFD code (Fluent) is performed to evaluate the BEM results (in 2D and 3D cases). The cavitation properties approximated by the present research study (especially with the reentrant jet model) are very close to the results of other experimental and numerical solutions. The need for a very short time (only a few minutes) to reach the desirable convergence and relatively good accuracy are the main advantages of this method.