  Molecular clouds often exhibit filamentary or sheet-like shapes. We compute
the free-fall time ($\tff$) for finite, uniform, self-gravitating circular
sheets and filamentary clouds of small but finite thickness, so that their
volume density $\rho$ can still be defined. We find that, for thin sheets, the
free-fall time is larger than that of a uniform sphere with the same volume
density by a factor proportional to $\sqrt{A}$, where the aspect ratio $A$ is
given by $A=R/h$, $R$ being the sheet's radius and $h$ is its thickness. For
filamentary clouds, the aspect ratio is defined as $A=L/\calR$, where $L$ is
the filament's half length and $\calR$ is its (small) radius, and the
modification factor is a more complicated, although in the limit of large $A$
it again reduces to nearly $\sqrt{A}$. We propose that our result for
filamentary shapes naturally explains the ubiquitous configuration of clumps
fed by filaments observed in the densest structures of molecular clouds. Also,
the longer free-fall times for non-spherical geometries in general may
contribute towards partially alleviating the "star-formation conundrum",
namely, that the star formation rate in the Galaxy appears to be proceeding in
a timescale much larger than the total molecular mass in the Galaxy divided by
its typical free-fall time. If molecular clouds are in general formed by thin
sheets and long filaments, then their relevant free-fall time may have been
systematically underestimated, possibly by factors of up to one order of
magnitude.
