In view of the fact that various gravitating and charged bodies may have si
ngular points on their surface, the problem of the effect of these singular
ities in the mass distribution on the behavior of potential arises. The ana
lytic representation for gravitational and electrostatic potentials of a un
iform elliptic cone in terms of ordinary integrals is derived. Generally, t
hese integrals are somewhat more complicated than the elliptic ones; howeve
r, they reduce to elementary functions in the case of a circular cone. The
arbitrariness in the way of truncating a cone manifests itself in the possi
bility of adding various harmonic polynomials. However, the singularity of
potential in the vicinity of the vertex of a cone is of an objective and un
ique character. (C) 2001 MAIK "Nauka/Interperiodica".