  The Gr\"obner basis technique for calculating Feynman diagrams proposed in
[O.V. Tarasov, Acta Physica Polonica, v. B29 (1998) 2655] is applied to the
two-loop propagator type integrals with arbitrary masses and momentum. We
describe the derivation of Gr\"obner bases for all integrals with 1PI
topologies and present elements of the Gr\"obner bases.
