In this paper a method for analytic modeling of three dimensional objects is introduced. The basic idea is to make use of the information obtained using computer vision to determine the Cartesian Coordinntes of a set of points existing on the surface of the object, this occurs through the use of range finding methods. These Coordinntes are fed to a computer program which computes the coefficients of the analytic equation such that the error in object modeling is minimum, this occurs by using the least mean square estimation for determining the coefficients of the fitting equation. The ellipsoid is the primitive used to model the objects. This method enables us to represent any object by a constant number of coefficients (9 coefficients) which is the number of coefficients in ellipsoid equation. Also, the waste volume will be reduced compared to the waste volume resulted when modeling the object with other models such as spheres or bounding boxes. Our primary coal is to provide a simple and accurate model for the objects in order to be able to design a collision free path for the robot arm while moving in its working space.