A detailed study into the rheology and microstructure of dense suspensions of initially spherical capsules is presented, where capsules are composed of a fluid-filled interior surrounded by an elastic membrane. This study couples a lattice-Boltzmann fluid solver to a finite-element membrane model creating a robust and scalable method for the simulation of these suspensions. A Lees–Edwards boundary condition is used to simulate periodic simple shear to obtain bulk rheological properties, and three-dimensional results are presented for capsules in the regime of negligible inertia, Brownian motion and colloidal interparticle forces. The simulation results focus on describing the suspension rheology as a function of the particle concentration and deformability, and relating these macroscopic rheological findings to changes at the particle level, i.e. the suspension microstructure. Several important findings are made: suspensions of deformable capsules are found to be shear thinning, and the initially compressive normal stresses associated with rigid spherical suspensions undergo rapid changes with moderate levels of particle deformation. These normal stress changes are particularly evident in the first normal stress difference, which undergoes a sign change at fairly minor levels of deformation, and the particle pressure, which decreases rapidly with increasing particle deformability. Changes in the microstructure as quantified by the single-body microstructure and the pair distribution function are reported. Also, results calculating particle self-diffusion are presented and related to changes in the normal stresses.