Computation of Grِbner bases for two-loop propagator type integrals

The Grِbner basis technique for calculating Feynman diagrams proposed in (Acta Phys. Pol. B 29(1998) 2655) is applied to the two-loop propagator type integrals with arbitrary masses and momentum. We describe the derivation of Grِbner bases for all integrals with 1PI topologies and present explicit content of the Grِbner bases.