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Within the framework of the configuration–interaction shell model, the present work applies three effective interactions to investigate the effects of the cross-shell excitation on F and Ne isotopes around <i>N</i> = 20, which are significantly proton–neutron asymmetric, and have different properties compared with the proton–neutron symmetric nuclei. It is shown that cross-shell excitation is necessary in order to reproduce separation energies, neutron drip lines, and low-energy levels of these isotopes. Furthermore, the cross-shell excitation of (0–5)<i>ħω</i> is suggested to be important in the description of ²⁹F and ³⁰Ne. However, the three interactions are insufficient in describing the bound structure of ^29,31Ne, and provide inconsistent shell structures and evolutions in the target nuclei. Their cross-shell interactions are suggested to be improved.