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The atomic masses of the three most abundant isotopes of strontium, 86,87,88Sr, and of the six most abundant isotopes of ytterbium, 170,171,172,173,174,176Yb, have been obtained from measurements of cyclotron frequency ratios of pairs of ions simultaneously trapped in a Penning trap. Our results, with one standard deviation uncertainty, are M(86Sr) = 85.909 260 730 9 (91) u, M(87Sr) = 86.908 877 497 0 (91) u, M(88Sr) = 87.905 612 257 1 (97) u, and M(170Yb) = 169.934 767 241 (18) u, M(171Yb) = 170.936 331 514 (19) u, M(172Yb) = 171.936 386 655 (18) u, M(173Yb) = 172.938 216 213 (18) u, M(174Yb) = 173.938 867 539 (18) u, M(176Yb) = 175.942 574 702 (22) u. These results have application to photon-recoil determinations of the fine-structure constant.