For a series of 1,4-butadiene (B)-styrene (S) symmetrical multiblock copolymers, BSB triblock, BSBSB pentablock, and BSBSBSB heptablock copolymers having the same block molecular weights and B/S composition, the rheological behavior and structure were examined in dibuty1 phthalate (DBP) at 25 degrees C. DBP is an S-selective solvent, i. e., a good solvent for the S blocks and a poor solvent for the B blocks. The copolymer concentrations C (= 22-25 wt %) were chosen to be just above (by 1 wt %) respective microphase separation concentrations. In a well-equilibrated state, the copolymer/DBP solutions formed a bcc lattice of the spherical domains of unsolved B blocks bridged by the S blocks (lattice-type network), thereby exhibiting elastic behavior under small strains. This lattice-type network was disrupted under steady shear to lose its elasticity, and the heaviest disruption occurred at an intermediate shear rate close to the B/S concentration fluctuation frequency. The elasticity was recovered after cessation of the preshear, and the time tr required for full recovery was insensitive to the preshear rate gamma pre, i. e., to the magnitude of the network disruption. This behavior suggested that the bridge-type S blocks crossing the flow planes were converted to loops under the preshear, and the re-formation of the bridges, requiring the B blocks to be thermally pulled out from their domain, was the rate-determining step for the recovery. In other words, tr of the multiblock copolymers appeared to be primarily determined by the gamma(pre)-insensitive thermodynamic barrier for transient mixing of the pulled out B block into the S/DBP matrix. For such multiblock copolymers, tr was found to increase strongly with increasing copolymer molecular weight, and a ratio of tr of the triblock, pentablock, and heptablock copolymers was close to 1: 5: 25. This ratio was consistent with the Rouse/reptation motion of the multiblock chain retarded by the B/S mixing barrier.