Can investment-specific technology (IST) shocks and the rigidity in the sectoral capital movements explain two of the international business cycles puzzles - the quantity anomaly and the international co-movement puzzle? I develop a two-country, two-sector and two-good (consumption and investment goods) IRBC model with IST and aggregate technology shocks, and with the rigidity in the sectoral capital movements. I compare its simulated moments with the new set of international business cycles facts developed in Khan (2008). Thus, I use the model to study the roles of IST shocks, trade in capital goods and the rigidity in the sectoral capital movements in explaining the international business cycle facts. The model can predict strong positive cross-country correlations of output and labor input. It can also predict a positive cross-country correlation of investment spending. The rigidity in the sectoral capital movements increases the cross-country correlations of output, labor and investment spending. Thus, this IRBC model resolves the international co-movement puzzle and makes a progress towards solving the quantity anomaly.