Recent observations made by the Herschel Space Observatory and the Planck Satellite have shown that molecular clouds are made by networks of filaments, shaped by interstellar turbulence and magnetic fields. We analyse the stability of filamentary molecular clouds with the help of cylindrical polytropic models with and without helical magnetic fields. We then focus on the growth of hydrodynamical density perturbations and the formation of sub-structures and fragments in pre-stellar cores.