With the aim of characterizing and gaining insight into the frequency response of cells suspended in a fluid medium and deformed with a controlled alternating electric field, a continuum-based analysis is presented for modeling electrodeformation (ED) via Maxwell stress tensor (MST) calculation. Our purpose here is to apply this approach to explain the fact that the electric field anisotropy and electrical conductivity ratio of the cytoplasm and the extracellular medium significantly impact the MST exerted on the cytoplasm-membrane interface. One important finding is that the modulation of electrical cues and MST force by the frequency of the applied electric field provides an extremely rich tool kit for manipulating cells. We show the extreme sensitivity of proximity-induced capacitive coupling arising concomitantly when the magnitude of the MST increases as the distance between cells is decreased and the spatial anisotropy becomes important. Moreover, our model highlights the strongly localized character of the electrostatic field effect emanating from neighboring cells and suggests the possibility of exploiting cell distribution as a powerful tool to engineer the functional performance of cell assemblies by controlling ED and capacitive coupling. We furthermore show that frequency has a significant impact on the attenuation-amplification transition of MST, suggesting that shape anisotropy has a much weaker influence on ED of the cell membrane compared to the anisotropy induced by the orientation angle itself.