  Using numerical simulations, we investigate the gravitational evolution of
filamentary molecular cloud structures and their condensation into dense
protostellar cores. One possible process is the so called 'edge effect', the
pile-up of matter at the end of the filament due to self-gravity. This effect
is predicted by theory but only rarely observed. To get a better understanding
of the underlying processes we used a simple analytic approach to describe the
collapse and the corresponding collapse time. We identify a model of two
distinct phases: The first phase is free fall dominated, due to the
self-gravity of the filament. In the second phase, after the turning point, the
collapse is balanced by the ram pressure, produced by the inside material of
the filament, which leads to a constant collapse velocity. This approach
reproduces the established collapse time of uniform density filaments and
agrees well with our hydrodynamic simulations. In addition, we investigate the
influence of different radial density profiles on the collapse. We find that
the deviations compared to the uniform filament are less than 10%. Therefore,
the analytic collapse model of the uniform density filament is an excellent
general approach.
