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It is now widely accepted that dense filaments of molecular gas are integralto the process of stellar birth. While numerical simulations have succeeded inreproducing filamentary structure in turbulent gas and analytic calculationshave predicted the formation of dense gas filaments via radial collapse, theexact process(es) that generate/s such filaments which then form prestellarcores within them, is unclear. In this work we therefore study numerically theformation of a dense filament using a relatively simple set-up of auniform-density cylinder in pressure equilibrium with its confining medium. Inparticular, we examine if its propensity to form a dense filament and further,to the formation of prestellar cores within this filament bears on thegravitational state of the initial volume of gas. We report a radial collapseleading to the formation of a dense filamentary cloud is likely when theinitial volume of gas is at least critically stable (characterised by theapproximate equality between the mass line-density for this volume and itsmaximum value). Though self-gravitating, this volume of gas, however, is notseen to be in free-fall. This post-collapse filament then fragments along itslength due to the growth of a Jeans-like instability to form prestellar coreslike \emph{beads on a string}. We suggest, dense filaments in typicalstar-forming clouds classified as gravitationally super-critical under theassumption of : (i) isothermality when in fact, they are not, and (ii) extendedradial profiles as against one that is pressure-truncated, thereby causingsignificant over-estimation of their mass line-density, are unlikely toexperience gravitational free-fall. The radial density and temperature profilederived for this post-collapse filament is consistent with that deduced fortypical filamentary clouds mapped in recent surveys of nearby star-formingregions.

Stability of filaments in star-forming clouds and the formation of prestellar cores in them