Abstract We have studied plane shear flow of nearly homogeneous assemblies of uniformly sized, spherical, cohesive particles in periodic domains under constant applied normal stress. Our focus has been on (a) exploration of the effect of inter-particle attractive forces on the flow behavior manifested by dense assemblies under constant applied normal stress, and (b) comparison of the rheological characteristics observed under constant-applied normal stress and constant-volume conditions. As a model problem, the cohesion resulting from van der Waals force acting between particles is considered. Simulations were performed for different strengths of cohesion, shear rates, and applied stresses. From each simulation, the volume fraction, shear stress and the average coordination number have been extracted. We find that cohesive assemblies sheared under constant applied normal stress shear differently from those sheared at constant volume only in the dynamic sense, while the time-averaged rheological characteristics are essentially indistinguishable. At constant volume, the fluctuations in shear stress are larger than, but have the same dependence on cohesion as under constant applied normal stress. This study has also exposed a pronounced dependence of the apparent coefficient of friction on particle volume fraction in the quasi-static flow regime.