A study is made of an unsteady flow of an incompressible viscous fluid with embedded small inert spherical particles contained in a tube of elliptic cross-section due to a periodic pressure gradient acting along the length of the tube. The solutions for the fluid velocity and the particle velocity are obtained for large and small times. It is shown that the effect of particles on the flow is significant in the small-time solution while the large-tlme solution shows no effect of the particles on the flow.