  The rigidity degree of a generator-cogenerator determines the dominant
dimension of its endomorphism algebra, and is closely related to a recently
introduced homological dimension -- rigidity dimension. In this paper, we give
explicit formulae for the rigidity degrees of all indecomposable modules over
representation-finite self-injective algebras by developing combinatorial
methods from the Euclidean algorithm. As an application, the rigidity
dimensions of some algebras of types $A$ and $E$ are given.
