It is important to understand the characteristics of material strength and fracture under the dynamic loading like as earthquakes to assure the integrity of welded structures. The characteristics of dynamic strength and fracture in structural steels and their welded joints should be evaluated based on the effects of the strain rate and the service temperature. It is difficult to predict or measure temperature rise history with the corresponding stress-strain behavior. In particular, material behaviors beyond the uniform elongation can not be precisely evaluated, though the behavior at large strain region after the maximum loading point is much important for the evaluation of fracture. In this paper, the coupling phenomena of temperature and stress-strain fields under the dynamic loading was simulated by using the finite element method. The modified rate-temperature parameter was defined by accounting for the effect of temperature rise under the dynamic deformation, and it was applied to the fully-coupled analysis between heat conduction and thermal elastic-plastic behavior. Temperature rise and stress-strain behavior including complicated phenomena were studies after the maximum loading point in structural steels and their undermatched joints and compared with the measured values.