Quantum chemical calculations show that metal-hydride molecules are more compact when they are placed inside a fullerene cage than when they are isolated molecules. The metalhydrogen bond distance in ZrH4 becomes 0.15 Å shorter when it is placed inside a C60 cage. Metal-polyhydride molecules with a large number of H atoms such as ScH 15 and ZrH16, which are not bound as isolated molecules, are predicted to be bound inside a fullerene cage. It is also shown that two TiH16 clusters are bound inside a bicapped (9,0) carbon nanotube. Possible ways to make metal-hydrides inside C60 and nanotubes are suggested.