Necessary conditions for the existence of stable particle concentration shocks in a fluidised suspension are derived on the basis of the particle bed model. It is shown that upwards travelling compression shocks always satisfy the stability conditions, in contrast to downwards travelling compression shocks, and all expansion shocks, which never do. The shock velocity is found to be proportional to the characteristic (dynamic) velocity for the particle phase, the proportionality constant being a simple function of the particle concentrations across the shock. A consequence of the stability analysis for slugging bens is that the interface separating a square-nosed gas-slug from the solid-slug immediately above represents a weak shock which travels upwards, relative to the solid-slug, at the dynamic wave speed for the particle phase.