A numerical study of the linear temporal stability characteristics of particulate suspension flow through a converging-diverging symmetric wavy-walled channel is considered. The basic flow is a superposition of plane channel flow of particulate suspension and periodic flow components arising due to the small amplitude sinusoidal waviness of the channel walls. The disturbance equations are derived within the framework of Floquet theory and solved using the spectral collocation method. The effects of small amplitude sinusoidal waviness of the channel walls and those of the presence of particles on the initial growth of the disturbances are examined. Two-dimensional stability calculations for particulate suspensions indicate the presence of fast growing unstable modes that arise due to the waviness of the walls. Neutral stability calculations are performed in the disturbances wavenumber-Reynolds number (α s -R e) plane, for the wavy channel with representative values of wavenumber (λ) and the wall amplitude to semi-channel height ratio ([InlineMediaObject not available: see fulltext.]) for different values of volume fraction density of the particles (C). It is observed that the critical Reynolds number for transition decreases with increase of [InlineMediaObject not available: see fulltext.] and C. However, the flow can be modulated by suitable wall excitation which in turn can stabilize the flow. © Springer-Verlag Wien 2005.