We present the results of calculation of the rates of tunnel ionization of N 2 and O 2 molecules from the ground and excited vibrational states by linearly polarized laser radiation. These data are necessary for the theoretical description of filamentation. For N 2 , we consider ionization from the 3σ g and 1π u shells, which give comparable contributions. For O 2 , we consider ionization from both the ground X 3 Σ − g and excited a 1 ∆ g electronic terms. We demonstrate that for N 2 , the ionization rate is maximum when the electric field vector of laser radiation is directed along the molecular axis (for 3σ g shell) or perpendicular to it (for 1π u shell), whereas for the O 2 molecule, for both electronic states considered, the rates have maxima when the angle between the electric field and molecular axis is equal to 45°.