Advances in tridimensional (3D) culture approaches have led to the generation of organoids that recapitulate cellular and physiological features of domains of the human nervous system. Although microelectrodes have been developed for long-term electrophysiological interfaces with neural tissue, studies of long-term interfaces between microelectrodes and free-floating organoids remain limited. In this study, we report a stretchable, soft mesh electrode system that establishes an intimate in vitro electrical interface with human neurons in 3D organoids. Our mesh is constructed with poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT:PSS) based electrically conductive hydrogel electrode arrays and an elastomeric poly(styrene-ethylene-butadiene-styrene) (SEBS) as the substrate and encapsulation materials. This mesh electrode can maintain stable electrochemical impedance in buffer solution under 50% compressive and 50% tensile strain. We have successfully cultured pluripotent stem cell-derived human cortical organoids (hCO) on this polymeric mesh for more than 3 months and demonstrated that organoids readily integrate with the mesh. Using simultaneous stimulation and calcium imaging, we show that electrical stimulation through the mesh can elicit intensity-dependent calcium signals comparable to stimulation from a bipolar stereotrode. This platform may serve as a tool for monitoring and modulating the electrical activity of in vitro models of neuropsychiatric diseases.