In this paper, single pile-up of screw dislocations formed against an obstacle situated at a distance from the interface of a bi-metallic medium and double pile-ups of screw dislocations formed between the interface of a bi-metallic medium and an obstacle situated at a distance from the interface have been analyzed. The distribution function for the single and double pile-ups of screw dislocations, the stress field ahead of the single pile-up of screw dislocations and the force acting on the leading dislocation of the double pile-up are derived for all values of the respective shear modulus ratio, G2/G1, such that 0<G2/G1<∞. © 1973 Noordhoff International Publishing.