Numerous biomedical and industrial applications require separation or sorting of particles in systems in which it is undesirable to allow particle adhesion to a surface, such as a centrifuge wall and a filter fibre. Such systems typically involve either adhesive particles which could easily foul such surfaces or very delicate particles as is the case with suspensions of biological cells. The current study explores an approach for particle separation based on exposure to an oscillating straining flow, which would be typical for peristaltic and other types of contractive wall motions in a channel or tube. We find that particles immersed in an oscillating straining flow are attracted to the nodal points of the straining field, a phenomenon which we refer to as ‘oscillatory clustering’. A simplified theory of this process is developed for cases with isolated particles immersed in an unbounded uniform straining flow, in which the particle motion is found to be governed by a damped Mathieu equation. Moreover, the drift velocity imposed on particles through oscillatory clustering is sufficient to suspend them against a downward gravitational force in a limit-cycle oscillatory path. Theoretical approximations for the average suspension height and oscillation amplitude are obtained. A discrete-element method (DEM) for colliding and adhesive particles is then employed to examine oscillatory clustering for more realistic systems in which particles collide with each other and with container walls. The DEM is used to examine oscillatory clustering of a particle suspension in an oscillating box and for standing peristaltic waves in a channel, both with and without particle adhesion forces and gravitational forces.