The orientation, microstructure, and rheology in non-Brownian shear flow were studied for suspensions of dicolloidal particles using a novel particle mesh Ewald Stokesian dynamics algorithm for anisotropic particles. Four different particle shapes were studied with dicolloids modeled as the union of two intersecting spheres. Dynamic simulations were conducted for periodic systems of 1000 particles for volume fractions phi=0.05-0.55. The suspension microstructure was disordered for all particle shapes at 0 <=phi <= 0.50, with some systems showing ordered microstructure at phi=0.55. The viscosity in the disordered state was similar for all particle shapes at equal volume fraction. Negative first and second normal-stress differences were found for phi <= 0.5, but positive values were observed for certain ordered systems at phi=0.55. Complex orientation behavior was observed as a function of volume fraction and particle shape. All particles showed an orientation shift toward the vorticity axis for phi >= 0.10. Certain shapes showed a shift away from the vorticity axis for phi <= 0.10. The high phi orientation dynamics were consistent with predictions based on the mobility tensor M(omega S) relating the angular velocity to particle stresslet. The orientation dynamics were dominated by the second normal-stress difference. The shift away from the vorticity axis for small phi was induced by migration away from orientations with large orientation fluctuations. (C) 2011 The Society of Rheology. [DOI: 10.1122/1.3569585]