The plane strain compression of a long symmetric strip consisted of a three layer material between rigid, parallel, rough plates is under consideration. Two possible geometrical configurations of the layers are examined (a) a viscoplastic material is situated between two layers consisting of a rigid/perfectly plastic material, (b) a rigid/perfectly plastic material lies between two viscoplastic layers. It is assumed throughout the paper that the viscoplastic law is bounded in that sense that it reaches its critical value (saturation stress) as the strain rate tends to infinity. Exploiting closed form solutions obtained, qualitative differences between them and the known from literature solutions for three layer material structure with classic viscoplastic material are discussed. Asymptotic behaviour of solutions in the vicinity of maximum friction surfaces is analysed for any configuration.