Two poly (tetramethylene glycols) (PTMG), molecular weight of 650 and 2000, with 4,4’-diphenylmethane diisocyanate (MDI) and poly(4,4’-diphenylsulphone terephthalamide) (PSA) prepolymer were polycondensated. Four different molar ratios of PTMG, MDI and PSA prepolymer were synthesized to form eight PU-PSA block copolymers. The mechanical properties including stress-strain and stress-relaxation measurements of each copolymer were discussed. The determined values of Young’s modulus E, Mooney-Rivlin relation elastic parameters C1 and C2, relaxation moduli E1(0) and E2(0), relaxation time tau 1 and tau 2 were used to estimate the effect of hard segment and soft segment domains on the mechanical behaviour of copolymers. It was found that PU-PSA block copolymers apparently displayed elastic properties, especially using the molecular weight 2000 of PTMG which exhibited more elastic behaviour.