  We give the monodromy representations of local systems of twisted homology
groups associated with Lauricella's system $F_D(a,b,c)$ of hypergeometric
differential equations under mild conditions on parameters. Our representation
is effective even in some cases when the system $F_D(a,b,c)$ is reducible. We
characterize invariant subspaces under our monodromy representations by the
kernel or image of a natural map from a finite twisted homology group to
locally finite one.
