We present experimental and numerical investigations of liquid evaporating from capillary tubes with round, square and polygonal cross-sections depending on the shape, size and position of their liquid-gas surface. Simulations are based on an Allen-Cahn type phase-field model, where the liquid-gas phase transition is governed by a function of the liquid-gas surface area, the distance of the surface to the entrance of the capillary and the concentration gradient in the gas phase. Experiments are conducted under defined initial and constant conditions. Throughout the whole experiment, temperature, relative air humidity and the weight of the liquid within the capillary tube are tracked continuously. We compare the computational evaporation curves with experimental data for square capillary tubes with inner side lengths of 1, 2 and 4 mm and find that the evaporation rate per cross-sectional area is inversely proportional to their inner side length. Furthermore, the model is applied to square, lens and drop shaped cross-sections and to square and star shaped cross-sections with rough inner walls. The results show that the model is applicable to any cross-section shape of straight capillary tubes and that the presented computational approach captures experimentally measured evaporation profiles very well. These findings are especially relevant for industrial applications such as the drying time of complex components after cleaning. (C) 2018 Elsevier Ltd. All rights reserved.