Falling ball rheometry of suspensions of spheres and rods is simulated with a boundary element method. Fully three‐dimensional simulations are performed to obtain static, configuration‐specific solutions of the particle motions as well as to track the particles in time. The relative viscosities of suspensions of spheres (both unimodal and bimodal in size distribution) with solid volume fractions up to 0.05 are obtained. The effect of the spheres on the pressure drop from the top to the bottom of the cylinder is also investigated. Up to 40 interacting particles are modeled. Suspensions of rods of aspect ratio 5 and 10 (volume fraction of solids equal to 0.01) are also modeled. Results agree with available laboratory measurements. Ensemble averages of configuration‐specific solutions give good approximations of the relative viscosity of suspensions, even though flow‐induced structure is not accounted for. Each configuration‐specific solution requires orders of magnitude less computation time than the dynamic analyses. Further computation time can be saved without loss of accuracy by modeling only those particles within roughly 10 ball radii (about one cylinder radius) of the falling ball.