We investigate the morphology of microphase separated domains in diblock copolymers where each chain consists of a stiff rod block and a flexible coil block. A simplified phenomenological model system is introduced, which is coarse-grained in terms of the local concentration difference between the two blocks and the local director field of the rod part. Computer simulations of this set of time-evolution equations in two dimensions show in the weak segregation regime that the elastic energy in the rod-block rich domains affects drastically the structures of microphase separated domains. A coil-to-rod transition is incorporated into the model system to examine the elastic and anisotropic effects. The effects of the external electric field are also investigated to control the domain morphology. (C) 2004 American Institute of Physics.