  Three-loop vacuum integrals are an important building block for the
calculation of a wide range of three-loop corrections. Until now, only results
for integrals with one and two independent mass scales are known, but in the
electroweak Standard Model and many extensions thereof, one often encounters
more mass scales of comparable magnitude. For this reason, a numerical approach
for the evaluation of three-loop vacuum integrals with arbitrary mass pattern
is proposed here. Concretely, one can identify a basic set of three master
integral topologies. With the help of dispersion relations, each of these can
be transformed into one-dimensional or, for the most complicated case,
two-dimensional integrals in terms of elementary functions, which are suitable
for efficient numerical integration.
