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Abstract We present calculations of the photoionization (PI) cross sections of rubidium and cesium Rydberg atoms for light with wavelengths ranging from the infrared to the ultraviolet, using model potentials from Marinescu et al (1994 Phys. Rev. A 49 982). The origins of pronounced PI minima are identified by investigating the free-electron wavefunctions. These include broad PI minima in the nS to ϵP PI channels of both Rb and Cs, with free-electron energy ϵ , which are identified as Cooper minima. Much narrower PI minima in the nD to ϵF channels are due to shape resonances of the free-electron states. We describe possible experimental procedures for measuring the PI minima, and we discuss their implications in fundamental atomic physics as well as in practical applications. Measurements of PI cross sections of Rydberg atoms may serve as a sensitive probe for many-electron interactions of the Rydberg electron in the atomic core region.