Puccinia graminis f. sp. tritici is the causal agent of stem rust of wheat. A new race designated TTKSK (also known as Ug99) and its variants (TTKST and TTTSK) are virulent to most of the stem rust resistance genes currently deployed in wheat cultivars worldwide. Therefore, identification, mapping, and deployment of effective resistance genes are critical components of global efforts to mitigate this threat. Multipathotype seedling tests demonstrated that resistance gene Sr35 is effective against the three TTKS variants and another broadly virulent race from Yemen, TRTTF. Two genetic maps of Sr35 are presented in diploid (Triticum monococcum) and two in hexaploid wheat (T. aestivum). The Sr35 resistance to TRTTF and RKQQC races was mapped in diploid wheat within a 2.2 to 3.1 cM interval on the long arm of chromosome 3Am between markers XBF483299 and XCJ656351. This interval corresponds to a 174-kb region in Brachypodium that includes 16 annotated genes. The Sr35 map location was confirmed in two backcross-derived hexaploid populations segregating for Sr35. Recombination between diploid and hexaploid chromosomes was 10-fold lower than between homologous chromosomes, but was sufficient to reduce the introgressed diploid segment. These maps provide markers closely linked to Sr35 that will be useful to accelerate its deployment and pyramiding with other stem rust resistance genes.