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Electric fields in polymeric insulation are calculated with the boundary element method (BEM) in the presence and absence of space charge. A 3-D version of the BEM software is employed to determine the profiles of divergent electric fields produced by metallic and semicon needles embedded in the polymeric insulation. It is shown that the value of the electric field in the insulation decreases rapidly and within 5 μm from the tip it is less than 50% of its initial value. The BEM can also provide 3D profiles of the electric field distributions in the presence of space charge.