We present a coupled immersed interface method-boundary element method (IIM-BEM) numerical technique that predicts the behaviour of deformable cells under the effect of both hydrodynamic and electrical forces. This technique is applied to the study of a hybrid electrical-mechanical trap for single-cell trapping. We report on the effect of different combinations of electrode positions and mechanical properties of the trap on the maximum loading and unloading Reynolds numbers. We also report on the effect that cells moving with the flow have on cells which have been already trapped in a cavity.