We discuss a simple model for creation of entanglement in a system composed of two two-level atoms interacting with a common environment. The role of the environment in entangling and disentangling of the atoms is explored. We demonstrate how the spontaneous decay of an initial excitation of the system can create a transient entanglement between the atoms. The opposite situation is also discussed where a spontaneous disentanglement of initially entangled atoms may exhibit some unusual features such as entanglement sudden birth, the phenomenon of entanglement sudden death and revival of entanglement. We provide a discussion of these unusual phenomena in terms of the density matrix elements of the system and show the connection of the phenomena with the threshold behaviour of the concurrence.