Crystallographic preferred orientations (CPOs) in deformed rocks are commonly interpreted as resulting from crystal plastic deformation mechanisms, where deformation is achieved by the movement of dislocations. In this paper we investigate the possibility of CPO-development by dissolution–precipitation creep or pressure solution. A numerical model is presented, which simulates the development of a grain aggregate that deforms by reaction-controlled dissolution–precipitation creep. Grains are simulated as rectangular boxes that change their shape by growth, or dissolution of their surfaces, depending on the normal stresses acting on the individual surfaces. Grains can also rotate due to an applied vorticity (for non-coaxial deformation) and if they have a non-equidimensional shape. For each strain increment, stress that is applied to the grains is the same for all grains, while individual grains deform and rotate by different amounts. A variety of CPOs develop at moderate strains, depending on the reaction rates of the different crystal-surfaces and type of deformation (uni-axial shortening, plane strain pure shear and simple shear). The modelling results confirm that dissolution–precipitation creep may play a role in CPO-development in rocks.