The measurement of critical current of superconducting conductors under applied tensile strain in high magnetic field [I-c,(B, epsilon] is essential for the application of Nb3Sn composite conductor in high field superconducting magnets. The large bore 20 T DC magnet at the NHMFL along with a device designed to apply tensile strain allows the I-c, (B, epsilon) measurement of about 100 mm long straight Nb3Sn composite wire. The superconducting wires are soldered to dog-bone shaped backing plates made of different materials. Our results show that the backing plate materials have significant effects on the measured I-c,(B, epsilon) behaviors. This paper also reports our recent experimental results on high current density Nb3Sn conductors.