With the aid of transfer matrices method, and personal computer, a computational research has been carried out on the properties of two models representing the axial electrostatic field of a quadrupole lens. One model is the well known bell-shaped field and the other is a modified form of the bell-shaped field. The path of the charged particles traversing the two fields has been determined by solving the trajectory equation of motion in Cartesian coordinates. A computer program has been written for this purpose. The optical properties of each axial electrostatic field have been computed with the aid of the beam trajectory along the lens length. Computer programs in Fortran 77 have been determining the various optical properties. The work has, been mainly concentrated on computing the focal length, spherical aberration, and chromatic aberration in both convergence and divergence planes for both field models. The Results have shown that the choice of an electrostatic quadrupole lens for a particular electron or ion optical system