A membrane connector or test probe having a group of connector or test probe contacts (14) in a central contact section of the membrane (12) is initially stretched by being axially displaced from the plane of the peripheral membrane support (10). The test probe is cause to contact the pads (43,44) of device (42) to be tested and is then moved through an over travel distance that tends to decrease the amount of the stretch of the membrane. This decrease in stretch effects a small amount of lateral radial displacement of the test probe contacts to provide a scrubbing action that enhances electrical engagement with a circuit chip pad that may have a poorly conductive oxide coating. Substantially all of the stretch of the membrane is caused to be concentrated in and about the central contact section of the membrane at which the test probe contacts are located. This is accomplished by causing the area of the membrane between its peripheral support and the central section to be substantially inextensible as by bonding an inextensible metallic shield (50) to these portions of the membrane.