Abstract. We study the shock dynamics for a recently proposed system of conservation laws (Murisic et. al [J. Fluid Mech. 2013]) describing gravity-driven thin film flow of a suspension of negatively buoyant particles down an incline. When the particle concentration is above a critical value, singular shock solutions can occur. We analyze the Hugoniot topology associated with the Riemann problem for this system, describing in detail how the transition from a double shock to a singular shock happen. We also derive the singular shock speed based on a key observation that the particles pilling up at the maximum packing fraction near the contact line.Key words. thin film, Riemann problem, conservation laws, singular shock AMS subject classifications. 35L65 35L67 74K351. Introduction. The flow of thin viscous suspension with particles has important application in science and industry, such as the Bostwick consistometer in the food industry [21] and spiral separator in the mining industry [18]. However, the continuum description of it is complicated due to the interplay of different physical effects including the increase of viscosity in the presence of particles [30,4], the settling of heavy particles due to gravity [12], and particle resuspension induced by shear [19,1]. Only recent studies have centered on particle-laden thin films down an incline with a free surface and moving contact lines.Zhou et al.[32] first derived a theory for shock dynamics by considering a gravitydriven film of a dense suspension of glass beads in oil with conserved volume. Three different regimes were observed depending on the inclination angle and initial particle concentration. At low inclination angles and concentrations, particles settle out of the flow leading to the stratification of the suspension with a clear fluid moving ahead of the particles; at intermediate angles and concentrations, the suspension stays wellmixed; and at high concentrations and inclination angles the particles concentrate at the contact line to form a particle-rich ridge. To model the problem, they treat the mixture as a Newtonian flow locally, and describe the two-phase flow by a depthaverage velocity depending on the effective viscosity of the suspension together with a relative velocity coming from the hindered settling. Shock solutions are obtained with an observation that the classical solution might cease to exist if the precursor thickness is smaller than a critical value. Cook et al. [8] revisited this model with a more complete explanation and more thorough characterization of the shocks solutions. A singular shock is expected without further analysis, and they observe that for this singular shock, the particle concentration exceeds the limits of the close packing, making the model invalid in high concentrations. Cook [7] later developed a model to identify a balance between hindered settling and shear-induced migration at the leading order in large scale physics for particle-liquid separation.Intensive experiments were carried out in [29] and [22]....