Stress-strain relations and strain-induced crystallization (SIC) of unvulcanized and vulcanized states of natural rubber (NR) and synthetic polyisoprene (IR) were studied using synchrotron X-ray at various temperatures from -50 to +75 degrees C. Unvulcanized IR is a polymer melt that shows a viscous response with yield stress that is related to entanglement and no SIC at 25 degrees C. However, unvulcanized IR shows SIC at 0, -25, and -50 degrees C. Entanglements in unvulcanized IR become pivots to align chains and induce crystals at low temperatures. On the other hand, unvulcanized NR shows SIC and stress upturns in stress-strain relations at 25 degrees C. Since a permanent set is observed after large extension and retraction, unvulcanized NR has a pseudo end-linked network. The pseudo end-linked networks make entanglements as permanent entanglements and show stress upturn and SIC. Vulcanization makes IR to a rubber which shows a stress upturn and SIC by chemical bond network. The stress of vulcanized NR and IR appear almost the same at strains less than 3.0, however the stress of vulcanized NR is much higher than vulcanized IR beyond strain 3.0. The onset strain of SIC of vulcanized NR is much smaller than vulcanized IR. This different behavior is caused by the pseudo end-linked network. The stress in stress-strain relation at higher temperatures is significantly lower than the stress at lower temperatures. This tendency does not seem to follow the theory of rubber elasticity. The onset of SIC delays the upturn of stress as a shoulder or plateau in the stress-strain relation. SIC contributes to the stress, even though the stress smoothly increases with strain. At higher strain, SIC become big network points to bind many chains and reduce the limit of extensibility. The effect of SIC and the limited extensibility to the stress is not distinguishable.