The pressure‐driven flow of a periodic suspension of two‐dimensional viscous drops in a channel that is bounded by two parallel plane walls is studied numerically using the method of interfacial dynamics, which is an improved version of the boundary integral method. The viscosity of the drops is assumed to be equal to that of the suspending fluid. The effects of capillary number, volume fraction, and number of rows are examined for ordered suspensions, where the drops are initially arranged in several rows on a hexagonal lattice. Results of dynamic simulations for random monodisperse suspensions with up to 12 drops per periodic cell are performed, and the salient features of the motion are discussed. It is found that, in all cases, the drops tend to migrate toward the centerline of the channel, forming either a single row or multiple rows. The effect of the instantaneous suspension microstructure on the effective viscosity is illustrated, and some important differences in the behavior of suspensions in pressure‐driven and shear‐driven flows are identified and discussed. Numerical evidence is presented, suggesting that the behavior of suspensions of high viscosity drops may be significantly different from that of suspensions of drops with small and moderate viscosity.