The subject of this paper is the computation of the first three moments of bounded regions imbedded in 2- and 3-dimensional Euclidean spaces. The method adopted here is based upon formulae derived elsewhere, that permit the computation of the said moments — volume, vector first moment and inertia tensor — via integration along the boundary. This is accomplished by the application of Gauss Divergence Theorem to planar and axially-symmetric 3-D regions. It is shown that a spline approximation of the boundary leads to explicit, readily implementable formulae. Two examples are included to illustrate the applicability of the procedure.