Layered Earth Green's functions play a central role in modeling the electromagnetic (EM) response of mineral exploration targets, both as the implicit basis of distributed source field computations and for integral equation and hybrid three-dimensional (3-D) formulations. They are computed as the Hankel transforms of analytic kernels. Computational precision can depend upon the choice of algebraically equivalent forms by which these kernels are expressed. Since 3-D modeling can require up to millions of Green's function evaluations, computational time can be significantly reduced by replacing direct point by point evaluation with 1-D cubic spline representations. Linear digital filters have proven to be a fast and accurate method of computing these Hankel transforms at the spline knots. For a given knot density, accuracy can be maximized by choosing a filter whose evaluation points correspond with the spline knots, which also allows the reuse of kernel evaluations. A new flow-through Hankel transform technique can further reduce computation times through the optimum use of previously evaluated kernels. ¿ 1999 American Geophysical Union