Simulations of dense suspensions of spherical solid particles in a Newtonian liquid carrier phase under simple shear flow have been performed. The simulations include solid-liquid mass transfer and (related) dissolution of the solids phase in the liquid. The interfaces between the solid particles and the liquid are fully resolved: in terms of the flow dynamics we apply a no-slip condition there and simulate the flow of the interstitial liquid by means of the lattice-Boltzmann method. In terms of mass transfer we solve a convection-diffusion equation for the solute concentration in the liquid with the saturation concentration imposed at the surface of the particles. The conditions are such that the flow is laminar (particle-bases Reynolds number significantly less than one). Peclet numbers are significant (order 100) which imposes strong demands on proper resolution of the mass transfer process. Results include dissolution times as a function of process conditions such as shear rate, solids loading, diffusivity and solubility. (C) 2014 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.