  We prove the uniform interpolation theorem in modal provability logics GL and
Grz by a proof-theoretical method, using analytical and terminating sequent
calculi for the logics. The calculus for G\"odel-L\"ob's logic GL is a variant
of the standard sequent calculus, in the case of Grzegorczyk's logic Grz, the
calculus implements an explicit loop-preventing mechanism inspired by work of
Heuerding.
