In this paper we show how a system consisting of solid particles sedimenting in a homogeneous or a stratified liquid can be simulated with Smoothed Particle Hydrodynamics (SPH). The solid particles are assumed to be sufficiently numerous that they may be treated as a continuous fluid. In the SPH formulation there are liquid SPH particles for each type of liquid and dust SPH particles for each type of dust. The liquids are treated as slightly compressible. We focus on the key features of drag and pressure terms and we show that dust, whether buoyant or sinking in homogeneous or stratified fluids, or sedimenting in a turbulent fluid, can be simulated efficiently and accurately. The SPH formulation allows us to simulate sedimentation within irregular boundaries, or in systems containing solid bodies such as stirrers with the lower cut-off of the turbulence given by the smoothing length. (C) 2015 Elsevier Ltd. All rights reserved.