It has been found that SBS block copolymers possess excellent tear strength at room temperature. However, tear strength is virtually zero at temperatures higher than the glass transition temperature of PS phase, ca. 95 degrees C. Tear strength at high temperatures can be improved by slight crosslinking of PB chains of SBS molecules with a small amount of dicumyl peroxides (DCP). The present work describes results of measurements of strength at high temperatures carried out on the DCP-cured SBS block copolymers. Fracture energies of DCP-cured specimens were determined using both a conventional tear test and a recently developed cutting test. The effect of crosslink density on fracture energy was investigated and correlated with microstructure. It has been found that specimens crosslinked with 0.01 phr DCP still possess relatively large tear strength at room temperature, about 10 kJ/m(2), when compared with uncrosslinked SBS specimens. Tear strength at high temperatures has been effectively enhanced to be about 100 to 1000 J/m(2), depending on the tearing rate. Specimens crosslinked with a higher level of DCP, however, showed a pronounced reduction of tear strength at room temperature, with tear strength of SBS specimens crosslinked with 1 phr DCP about one-tenth of that of neat SBS. The threshold fracture energy of crosslinked SBS copolymers is found to be proportional to the square root of the molecular weight between chemical crosslinks in the PB phase, which is in accord with the theory of Lake and Thomas. Moreover, from the results of cutting test, it is found that the majority, about 70%, of the fracture energy of neat SBS specimens comes from the rupture of the long PB chains of SBS molecules. The rest is the contribution from the energy associated with the PB/PS interface.