The effect of the strain rate and draw temperature on the mechanical behavior of ethylene vinyl alcohol (EVOH) and EVOH composites was analyzed. When EVOH is stretched at moderate strain rates, evidence of strain-induced crystallization and recrystallization was observed. Higher strain rates produced less structural variation because the homogeneous flow of the chains and the crystalline perfection are restricted due to the rapid drawing. In reference to the drawing temperature, EVOH showed a diffusive yielding, and the mechanical parameters were reduced due to the softening of the crystalline region. For EVOH composites, the filler hinders the molecular mobility, causing an increase in the strength and restricting the plastic flow. However, the higher temperature, higher molecular mobility, and ductility are not so affected by the filler content.