The invention provides an electrical connection device for connecting high density contacts of large scale integrated circuits (LSI) and serves to establish electrical connection between the contact areas (15) of the circuit network (14) on a substrate (11) for supporting integrated circuit devices (12) and the contact pads (18) of a conductor network (17) on a printed circuit card (13). The electric connection device comprises a plurality of conductive elements disposed within a housing (26) extending in a given direction. The conductive elements are electrically insulated one from the other and have contacts which are exposed through slots in the housing to connect to the areas (15) and pads (18). The conductive elements (29) are stacked in the given direction and are formed each with a conductor sheet (30) provided with two contact surfaces (31a, 32a) elastically movable in a plane normal to the given direction independently of the surfaces of contact of neighboring sheets. The conductor sheet are supported on elastically deformable rolls extending the length of the support means which enable the contact surfaces to be displaced and compensate for deformities in the substrate and manufacturing tolerances.