The stability of colloidal dispersions is of crucial importance because the properties of dispersions are strongly affected by the degree of coagulation. Whereas the coagulation kinetics for quiescent (i.e., nonstirred) and diluted systems is well-established, the behavior of concentrated dispersions subjected to shear is still not fully understood. We employ the discrete element method (DEM) for the simulation of coagulation of concentrated colloidal dispersions. Normal forces between interacting particles are described by a combination of the Derjaguin, Landau, Verwey, and Overbeek (DLVO) and Johnson, Kendall, and Roberts (JKR) theories. We show that, in accordance with the expectations, the coagulation behavior depends strongly on the particle volume fraction, the surface potential, and the shear rate. Moreover, we demonstrate that the doublet formation rate is insufficient for the description of the coagulation kinetics and that the detailed DEM model is able to explain the autocatalytic nature of the coagulation of stabilized dispersions subjected to shear. With no adjustable parameters we are able to provide semiquantitative predictions of the coagulation behavior in the high-shear regions for a broad range of particle volume fractions. The results obtained using the DEM model can provide valuable guidelines for the operation of industrial dispersion processes.