The Casimir surface force density F on a dielectric dilute spherical ball of radius a, surrounded by a vacuum, is calculated at zero temperature. We treat (n-1) (n being the refractive index) as a small parameter. The dispersive properties of the material are taken into account by adopting a simple model for the dispersion relation, involving a sharp high frequency cutoff at omega = omega(0). For a nondispersive medium there appears (after regularization) a finite, physical force F-nondisp which is repulsive. By means of a uniform asymptotic expansion of the Riccati-Bessel functions we calculate F-nondisp UP to the fourth order in 1/v. For a dispersive medium the main part of the force F-disp is also repulsive. The dominant term in F-disp is proportional to (n-1)(2)omega(0)(3)/a, and will under usual physical conditions outweigh F-nondisp by several orders of magnitude. [S0556-2821(99)05281-2].