We present a numerical calculation of the tunnelling time of electrons confined in double-barrier structures performed by means of the so-called stabilization method, widely used in quantum chemistry. From the stabilization graphs we find the resonance energy and its width. The method is especially appropriate for treating the case of double-barrier structures (symmetric or non-symmetric) because it allows one to calculate separately the two different tunnelling times (to the left and to the right of the quantum well) contributing to the total lifetime of a resonant level. We use the effective-mass theory. The behaviour of the tunnelling time under applied bias is also investigated and the results are compared with the ones obtained by two alternative approaches, the quasi-classical approximation and the transmission coefficient analysis, respectively. A good agreement between the three methods is obtained for the cases analysed. Finally, the stabilization method as applied here can be employed in the field of scanning tunnelling microscopy of absorbed atoms or molecules where a double-barrier potential also serves as a model for the problem.