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We give the monodromy representations of local systems of twisted homologygroups associated with Lauricella's system $F_D(a,b,c)$ of hypergeometricdifferential equations under mild conditions on parameters. Our representationis effective even in some cases when the system $F_D(a,b,c)$ is reducible. Wecharacterize invariant subspaces under our monodromy representations by thekernel or image of a natural map from a finite twisted homology group tolocally finite one.

The monodromy representations of local systems associated with Lauricella's $F_D$