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This paper proposes a new skeleton based parametric representation of freeform shell-like solid objects - Ball B-Spline Surfaces (BBSSs) and their fundamental properties and algorithms. BBSSs are generalizations of ball B-Spline curve from one parameter variable to two parameter variables. BBSSs directly define objects in B- Spline form, unlike a procedure method like sweeping. BBSSs describe not only every point inside 3D solid objects, but also provides their center surface (skeleton). So the representation is more flexible for modeling, manipulation and deformation.