The air-water two-phase flow across a staggered tube bundle at a pitch-to-diameter ratio of 1.4 is analyzed by an incompressible two-fluid model using the upstream finite element method proposed in a prior study. The Reynolds number, based on the tube diameter and the volumetric velocity of the liquid phase at the tube gap, is 41 000, and the volumetric fraction of the gas phase upstream of the bundle g0 ranges from 0 to 0.15. The calculated flows exhibit unsteady and complicated behavior irrespective of g0. The change in the drag coefficient of a tube in the bundle due to g0 agrees with the experimental result. The distribution of the volumetric fraction of the gas phase around the tube is also in good agreement with the measurement trend. These results indicate that the finite element method is usefully applicable to the two-phase-flow analysis in staggered tube bundles. It is also clarified that the unsteady flows are attributable to the occurrence and movement of vortices of both phases around the tubes.