High-power high-temperature superconducting (HTS) machines and devices require the use of high-current cables such as an HTS Roebel cable. An HTS Roebel cable comprising 15 strands of 5 mm width has a cable I-c in excess of 1.5 kA at 77 K, and can be wound directly into a variety of coil geometries. Many potential applications will subject the cable to large forces, and therefore there is a need to characterize the performance of HTS Roebel cable under tensile stress. We describe the experimental approach used to perform I-c measurements at 77 K on samples subjected to incrementally increasing values of tensile strain. In particular, we note the requirement for cable contacts that promote equal current sharing between strands. We present data showing the degradation of I-c under tensile stress for 15/5 cable and 5 mm coated conductor HTS strand, and give values for the irreversible stress limit for strand and cable. We compare these data with values obtained for 12 mm coated conductor HTS wire. We also show that the ultimate tensile strength of the Roebel cable can be found from a simple linear summation of the strands. However, the irreversible strain limit for the 15/5 HTS Roebel cable is lower than that of an isolated strand, due to the confinement of out-of-plane twisting for strands wound into a cable.