In the paper , we give the full system of equations modelling the motion of a fluid/viscoelastic solid system, and obtain a differential model similar to the so-called Oldroyd model for a viscoelastic fluid. Moreover, existence results in bounded domains are obtained. In this paper we extend the results in  to unbounded domains. The unique solvability of the system of equations is established locally in time and globally in time with so-called smallness restrictions. Moreover, existence of a weak solution is treated.