Air-water two-phase flows around a rectangular cylinder located in vertical upward flows are analyzed by an incompressible two-fluid model using the two-dimensional upstream finite element method proposed earlier. The Reynolds number, based on the cross-stream width of the cylinder and the free-stream velocity of the liquid phase, is 2.0 x 104, and the volumetric fraction of the gas phase upstream of the cylinder g0 ranges from 0 to 0.075. Three kinds of cylinders with the thickness-to-width ratios D/B of 0.5, 1, and 1.5 are employed. The calculated flows exhibit unsteady behavior with the von Kármán vortices shedding from the cylinder into the wake at every g0 value. The volumetric fraction of the gas phase is higher in the wake and achieves maximum value at the center of the vortices, where the pressure reaches its minimum value. The flow field and the vortex-shedding frequency are greatly affected not only by the g0 value but also by the D/B ratio.