During the thickening process of sludges with intermediate to high solid concentrations three settling regimes are typically encountered, namely, zone, transition, and compression regimes. Recent studies have indicated that the validity of Kynch's formulation, which is the most widely used for sizing settling basins, is limited to the zone settling regime. His formulation is based on the solids mass balance equation and does not consider the role of the rising sediment at the bottom of the settling basin. This limitation is rectified in this study by using a dynamic equation, a second order non - linear partial differential equation for the effective pressure of the solid particles. The equation is solved by using the finite element method. The so obtained effective pressure is used with an appropriate constitutive relation for the volume fraction of solids, to determine the variation of the solids content within the deposited material, and the height of the falling mudline. / Master of Science