The effect of capillary cross-section geometry on evaporation is investigated in terms of the meniscus shape, evaporation rate and evaporation-induced flow for circular, square and rectangular cross-sectional capillaries. The shapes of water and ethanol menisci are not much different from each other in square and rectangular capillaries even though the surface tension of water is much larger than that of ethanol. On the other hand, the shapes of water and ethanol menisci are very different from each other in circular capillary. The averaged evaporation fluxes in circular and rectangular capillaries are measured by tracking the meniscus position. At a given position, the averaged evaporation flux in rectangular capillaries is much larger than that in circular capillary with comparable hydraulic diameter. The flow near the evaporating meniscus is also measured using micro-PIV, so that the rotating vortex motion is observed near the evaporating ethanol and methanol menisci except for the case of methanol meniscus in rectangular capillary. This difference is considered to be due to the existence of corner menisci at the four comers.