Rheological and structural behavior was examined for a series of symmetric styrene (S)-isoprene (I)-styrene (S) multiblock copolymers of (SIS)(p)-type (p = 1, 2, 3, and 5 corresponding to tri-, penta-, hepta-, and undecablock) in n-tetradecane (C14), a selective solvent that dissolves the I block and precipitates (but swells) the S block. The molecular weights of respective blocks were almost identical for these copolymers (M-I congruent to 40K for I block; M-s congruent to 20K and 10K for inner and outer S blocks, respectively). At 20 degrees C, the (SIS)(p)/C14 systems with the copolymer concentration C = 30 wt % formed a bcc lattice of spherical S domains (with T-g,T-PS = 38 degrees C) embedded in the I/C14 matrix. Under small shear and elongation in the linear regime, the systems exhibited gel like elasticity sustained by the I blocks connecting the S domains. This linear elastic behavior, being associated with affine displacement of the S domains as revealed from small-angle X-ray scattering (SAXS) under small elongation, was very similar for all (SIS)(p)/C14 systems having the same C. In contrast, a remarkable difference was found for those systems under large (but slow) elongation: The maximum stretch ratio at rupture, lambda(max), significantly increased with the repeating number p of the SIS units, lambda(max) congruent to 2.1-: 1.7, 2.2, 6.6, and >= 90 for p = 1, 2, 3, and 5, respectively. In particular, lambda(max) >= 90 for p = 5 was much larger compared to the full-stretch ratio of the trapped entanglement strand (lambda(full-ent) congruent to 14) and even to the full-stretch ratio of the (SIS)(5) copolymer chain as a whole (lambda(full-copolymer) congruent to 40). For investigation of the structural origin of such remarkably high extensibility of the undecablock system (p = 5), SAXS and rheological tests were made under elongation followed by reversal. The tests revealed affme stretching of the lattice (affme displacements of the S domains) and negligible stretching of the lattice and the significant stress strain hysteresis were observed. Thus, under large elongation, some of the S blocks were pulled out from their domains and transferred to the other S domains at 20 degrees C, the experimental temperature not significantly lower than T-g,T-PS 38 degrees C) of the swollen S domains, to allow the system to deform plasto-elastically. This deformation differed from unrecoverable plastic flow, as evidenced from spontaneous, full recovery of the size, shape, and SAXS profile of the (SIS)(5)/C14 specimen being kept at rest (without load) at 20 degrees C for a sufficiently long time after the elongation. This recovery strongly suggests that the material preserved some memory of initial connection between the (SIS)(5) chains through the S domains, in particular in the direction perpendicular to the elongation, and the corresponding physical network still percolated the whole material even under large elongation. This argument in turn provides us with a clue for understanding the difference of lambda(max) for the series of (SIS)(p)/C14 systems. The full percolation can survive and the material can stand with the elongation if at least two PS blocks, on average, remain intact (not pulled out) in each (SIS)(p) copolymer backbone. The probability of having such intact S blocks obviously increases with the repeating number p of the SIS units, which possibly resulted in the observed difference of lambda(max).