The neutron radiative capture cross sections have been measured for the stable isotopes of Rb (mass numbers 85, 87) and Sr (mass numbers 84, 86, 88) using the activation technique, by observing the $$\gamma $$ rays emitted in the decays of the radionuclides produced in neutron irradiation. Values are reported for both the thermal cross sections and the resonance integrals. Internal consistency of the deduced values has been obtained where possible by measuring several radioisotopes from the same sample as well as by irradiating at several different reactor sites that have different mixtures of thermal and epithermal neutrons. Experimental values of the thermal cross sections are compared with values calculated from the known resonances. Isomer ratios are deduced and compared with values calculated from a phenomenological model. Also reported are spectroscopic studies of Rb and Sr radionuclides leading to improved values for the energy of $$\gamma $$ rays emitted in the decays of $$^{{86}}\hbox {Rb}$$ , $$^{{{85g}}} \hbox {Sr}$$ , and $$^{\mathrm {89}}\hbox {Sr}$$ . The half-life of $$^{{{87m}}}\hbox {Sr}$$ has been remeasured in order to resolve the conflict between two precise but discrepant values reported in the literature.