This work demonstrates how a stochastic model can be implemented to obtain a realistic description of the interaction of a biological cell with an external magnetic or electrical fields. In our model formulation, the stochasticity is adopted by introducing various levels of forcing intensities in model parameters. The presence of noise in nuclear membrane capacitance has the most significant effect on the current flow through a biological cell. The increasing amount of data reporting on the biological effects of magnetic and electric fields is leading researchers to understanding of how important it is to fully understand the mode of action of magnetic or electric fields to living organisms. Indeed, even if the perturbations of biological systems by magnetic or electric fields are sublethal at shorter times of exposure, these perturbations could, especially at longer times of exposure, evolve into a progressive accumulation of modifications, whose ultimate effects still need to be clarified.