Hiya
It depends on which shuttle you buy, the G2, G5 & G6 chassis will only take a single slot graphics card unless you modify the case. The P2 chassis will take a double slot card. The OcUK ATI Radeon HD 3870 XT 512MB GDDR4 TV-Out/Dual DVI (PCI-Express) would only fit in the P2 chassis without modification. The 9600 would fit in either. If you want to fit a HD 3870 in a G chassis, have a look at the Sapphire HD 3870 Atomic, it's a single slot card.