The dynamical evolution of entanglement between two systems of two-level atoms interacting with a common heat reservoir is investigated and the entanglement between subsystems is described by using the concurrence entanglement. By means of numerical calculations, the effects of initial state and interatomic distance on the two-atom-entanglement evolution as well as the effects of coupling strength and detuning on the two-subsystem-entanglement evolution are analyzed. The results show that, when the interatomic distance is relatively small, the rapid oscillation phenomenon appears no matter whether the initial state is symmetrical state or anti-symmetrical state. The interaction between atoms decreases with the increase of interatomic distance. Under strong coupling, the phenomena of entanglement death and entanglement recovery appear. The entanglement transfer from atoms to heat reservoir is suppressed when the increasing detuning.