Cosmic-ray-produced (CP) nuclides with half-lives shorter than 21h were measured in rainwater by ultra-low-background gamma spectrometry at Ogoya Underground Laboratory. As levels of CP nuclides are extremely low and their half-lives are very short, quick sampling methods for a large volume of rainwater and rapid chemical separations by ion exchange method were developed. The nuclides measured were short-lived (24)Na, (28)Mg, (38)S, (38)Cl, (39)Cl, as well as nuclides with longer half-lives (7)Be and (22)Na. The number of atoms of CP nuclides in rainwater were evaluated to range from 30 to 1500L(-1) for (24)Na (n=16, mean; 520 [6.7mBqL(-1)]), 80 to 600L(-1) for (28)Mg (n=13, mean; 260 [2.4mBqL(-1)]), 400 to 1900L(-1) for (39)Cl (n=6, mean; 1200 [250mBqL(-1)]), 1x10(6) to 4x10(7)L(-1) for (7)Be (n=16, mean; 7x10(6) [1.05BqL(-1)]) and 2x10(3) to 1x10(5)L(-1) for (22)Na (n=9, mean; 2x10(4) [0.2mBqL(-1)]).