Abstract: The main feature of flows of electrorheological (ER) fluids is the deformation of chain like structures of particles. The simplest of all structures in ER fluids is a single ER chain. There are two kinds of deformation of chains in ER devices: those produced by moving electrodes such as in ER clutches, and those produced by flow such as in ER valves.Due to the relative movement between basic fluids and ER chains, the analysis of ER chains under flow is more challenging. In this paper an analytical study o...