It is now widely accepted that dense filaments of molecular gas are integral to the process of stellar birth. While numerical simulations have succeeded in reproducing filamentary structure in turbulent gas and analytic calculations have predicted the formation of dense gas filaments via radial collapse, the exact process(es) that generate/s such filaments which then form prestellar cores within them, is unclear. In this work we therefore study numerically the formation of a dense filament using a relatively simple set-up of a uniform-density cylinder in pressure equilibrium with its confining medium. In particular, we examine if its propensity to form a dense filament and further, to the formation of prestellar cores within this filament bears on the gravitational state of the initial volume of gas. We report a radial collapse leading to the formation of a dense filamentary cloud is likely when the initial volume of gas is at least critically stable (characterised by the approximate equality between the mass line-density for this volume and its maximum value). Though self-gravitating, this volume of gas, however, is not seen to be in free-fall. This post-collapse filament then fragments along its length due to the growth of a Jeans-like instability to form prestellar cores like \emph{beads on a string}. We suggest, dense filaments in typical star-forming clouds classified as gravitationally super-critical under the assumption of : (i) isothermality when in fact, they are not, and (ii) extended radial profiles as against one that is pressure-truncated, thereby causing significant over-estimation of their mass line-density, are unlikely to experience gravitational free-fall. The radial density and temperature profile derived for this post-collapse filament is consistent with that deduced for typical filamentary clouds mapped in recent surveys of nearby star-forming regions. ; Comment: 18 pages, 17 figures (This is a redacted abstract, made compatible with the Astroph character limit); To appear in Publications of Astronomical Soc. of Australia(PASA)