We present the complex absorbing potential (CAP) method to investigate the Stark effect in hydrogen and lithium. The numerical technique as applied to calculations of Stark shifts and widths yields an appealing, simple and powerful tool for the computation of resonance parameters of the scattering processes. The feasibility and accuracy of the present method are demonstrated by the numerical evidence of the Stark shifts and widths of H atom ground and excited states. The results agree satisfactorily with the available results in the literature. Moreover, the method provides unambiguous advantages over other existing methods for the calculation of resonance parameters in a many-electron system and is illustrated for the low-lying states of the Li atom under the influence of external DC electric fields. Some new results are reported.