Reliable extracellular stimulation of neuronal activity is the prerequisite for electrical interfacing of cultured networks and brain slices, as well as for neural implants. Safe stimulation must be achieved without a damage of the cells. With respect to a future application of highly integrated semiconductor chips, we present an electrophysiological study of capacitive stimulation of mammalian cells in the geometry of adhesion on an insulated titanium dioxide/silicon electrode. We used HEK293 cells with overexpressed Na_V1.4 channels and neurons from rat hippocampus. Weak biphasic stimuli of falling and rising voltage ramps were applied in the absence of Faradayic current and electroporation. We recorded the response of the intra and extracellular voltage and evaluated the concomitant polarization of the attached and free cell membrane. Falling ramps efficiently depolarized the central area of the attached membrane. A transient sodium inward current was activated that gave rise to a weak depolarization of the cell in the order of 1 mV. The depolarization could be enhanced step by step by a train of biphasic stimuli until self-excitation of sodium channels set in. We applied the same protocol to cultured rat neurons and found that pulse trains of weak capacitive stimuli were able to elicit action potentials. Our results provide a basis for safe extracellular stimulation not only for cultured neurons on insulated semiconductor electrodes, but also more generally for metal electrodes in cell culture and brain tissue.