Abstract Properties of the hierarchical structures of interstellar molecular clouds are discussed. Particular attention is paid to the statistical correlations between velocity dispersion and size, and between the magnetic field strength and gas density. We investigate the formation of some hierarchical structures with the help of numerical MHD simulations using the ENLIL code. The simulations show that the interstellar molecular filaments with parallel magnetic field and molecular cores can form via the collapse and fragmentation of cylindrical molecular clouds. The parallelmagnetic field halts the radial collapse of the cylindrical cloud maintaining its nearly constant radius ~0.1 pc. The observed filaments with perpendicularmagnetic field can form as a result of themagnetostatic contraction of oblate molecular clouds under the action of Alfvén and MHD turbulence. The theoretical density profiles are fitted with the Plummer-like function and agree with observed profiles of the filaments in Gould’s Belt. The characteristics of molecular cloud cores found in our simulations are in agreement with observations.