We consider materials whose mechanical integrity is the result of a ja
mming process. We argue that such media are generically ''fragile,'' u
nable to support certain types of incremental loading without plastic
rearrangement. Fragility is linked to the marginal stability of force
chain networks within the material. It can lead to novel mechanical re
sponses that may be relevant to (a) jammed collsids and (b) poured san
d. The crossover from fragile to elastoplastic behavior is explored.