Unstable interaction between shear layers that form in the wake of an isolated building exposed to wind can drive natural pumping ventilation in windward and leeward facing rooms with two or more horizontally separated openings. This paper presents an experimental and numerical study of pumping ventilation in a three-story cubic building with two leeward openings in its middle floor. Reduced-scaled measurements were performed in the University of Gävle atmospheric-boundary-layer wind tunnel. The ventilation mechanism was investigated using smoke visualization, hot wire anemometry and particle image velocimetry. Effective ventilation rates were obtained using a tracer gas decay method. Experimental results confirmed that pumping ventilation is a 3D oscillatory unstable phenomenon with periodic behavior over several oscillation cycles. Measured flowrates show a linear relation between the effective ventilation rate and window separation. The numerical simulations used two turbulence modeling approaches: unsteady Reynolds-averaged Navier-Stokes (URANS) and large eddy simulation (LES). Both URANS and LES could predict vortex shedding frequency with an error below 5%. LES showed a good agreement with the measured ventilation rates, with an error below 10%, while URANS underestimated ventilation rates by at least 40%. The ventilation efficiency, obtained by LES, ranged between 0.60 and 0.75 (for the case with larger window separation). The results show that LES may be a suitable simulation approach for pumping ventilation. In contrast, URANS cannot simulate pumping ventilation.