The preparation of polymer foams is strongly influenced by the rheological properties of the polymer matrix. Strain-hardening polymers are usually used for preparation of closed-cell foams. On the contrary, strain-softening in melt elongation favours the rupture of cell walls and consequently promotes the preparation of open-celled foams. In this work, we focus on diblock copolymers in the microphase-separated state. Our recent works have shown that diblock copolymers are associated with strain-softening in melt elongation and thus are ideally suited for fabrication of open-celled foams [1,2]. In this study, we elucidate the potential of a polystyrene-block-poly(4-vinylpyridine) and a polystyrene-block-poly(4-methylstyrene) diblock copolymer for preparing open-celled foams which were synthesized using the technique of sequential anionic polymerization. The properties of these foams are compared with foams of polystyrene and poly(4-methylstyrene). The technique of batch foaming using water and carbon dioxide as blowing agents is applied for foam preparation. In shear, the steady-state viscosity of the diblock copolymers of this study decreases with shear rate (structure-viscous behaviour). Our elongational experiments show that the diblock copolymers are associated with the phenomenon of strain-softening. The transient extensional viscosity in simple elongation agrees with the threefold of the shear viscosity. Our batch foaming experiments reveal that open-celled polymer foams using water and carbon dioxide as blowing agents can be prepared at appropriate processing conditions. On the contrary, the use of a strain-hardening polystyrene leads to a closed-celled foam. [1] M. Schulze, U.A. Handge, S. Rangou, J. Lillepärg, V. Abetz, Polymer 70, 88-99 (2015). [2] M. Schulze, U.A. Handge, V. Abetz, Polymer 108, 400-412 (2017).