  Solar filaments are cold and dense materials situated in magnetic dips, which
show distinct radiation characteristics compared to the surrounding coronal
plasma. They are associated with coronal sheared and twisted magnetic field
lines. However, the exact magnetic configuration supporting a filament material
is not easy to be ascertained because of the absence of routine observations of
the magnetic field inside filaments. Since many filaments lie above weak-field
regions, it is nearly impossible to extrapolate their coronal magnetic
structures by applying the traditional methods to noisy photospheric
magnetograms, in particular the horizontal components. In this paper, we
construct magnetic structures for some filaments with the regularized
Biot--Savart laws and calculate their magnetic twists. Moreover, we make a
parameter survey for the flux ropes of the Titov-Demoulin-modified model to
explore the factors affecting the twist of a force-free magnetic flux rope. It
is found that the twist of a force-free flux rope is proportional to its axial
length to minor radius ratio, and is basically independent of the overlying
background magnetic field strength. Thus, we infer that long quiescent
filaments are likely to be supported by more twisted flux ropes than short
active-region filaments, which is consistent with observations.
