The mechanical properties and the structural transformations occurring during deformation of some commercial grades of ethylene/1-octene multiblock copolymers (OBCs) obtained from chain shuttling technology are analyzed. The samples are characterized by a statistical multiblock architecture, where soft and amorphous blocks with high octene concentration (approximate to 18.9 mol %) alternate with hard and crystalline blocks with low octene concentration (approximate to 0.5 mol %). The length of blocks (BL) and the number of blocks/chain (NB) change from chain to chain according to a statistical distribution. The selected samples have molecular mass in the range 85-130 kg/mol, percentage of hard segments in the range 15-27%, and a melting temperature of approximate to 120 degrees C. The average molecular masses of the hard blocks M-H and soft blocks M-S are in the ranges 2-3 kg/mol and 6-15 kg/mol, respectively, whereas the number of blocks/chain is in between 2 and 17. Even though the samples are characterized by similar octene concentration, small difference in molecular mass, and fractional content of hard blocks, they show remarkable differences of mechanical properties, depending on the average BL and NB values, encompassing from those of strong elastomers, in the case of samples with low block length and high number of blocks/chain, to those of soft elastomers, in the case of samples with high block length and low number of blocks/chain. The differences in the mechanical properties of OBC samples are amplified by stretching at high temperatures. Not previously stretched films obtained by compression molding show only partial recovery of the initial dimensions in mechanical cycles of stretching and releasing the tension, with values of recovered strain higher than 50% at 25 degrees C. However, the resultant specimens obtained by release of the tension show good elastomeric properties in a wide deformation range at 25 degrees C and, in the case of the samples with high strength, also at 60 degrees C. Fiber diffraction analysis reveals that by stretching at high deformation the orientation of the crystals is accomplished by mechanical melting and formation of an oriented amorphous phase, namely, involving the hard segments extracted from the crystals. Upon releasing the tension recrystallization occurs, and the high degree of orientation achieved by the crystals and amorphous phase is lost.