Abstract: In this paper.the boundary value problems of plane problems with a simply-ormultiply-connected domain for isotropic linear visca-elosticity are first established byterms of Airy stress function F(X_u t). Secondly some identity relations betweendisplacements and stresses for plane problems of sisco-and elasticity are discussed indetait and some meaningful conclusions are obtained As an example the deformationresponse for viscoelastic plate with a small circular hote at the center is analyzed undera uniasial uniform extension.