We investigate theoretically and numerically the diffusion-limited evaporation of aliquid deposited on a fiber in two configurations: a sleeve and a axisymmetric barrel-shapeddroplet. For a sleeve, the local flux depends on both the aspect ratio and the smallest length ofthe problem. By using analytical calculations and 3D finite elements simulations, we predict adivergence of this flux further localized at the edge as the aspect ratio increases. The evaporationof axisymmetric drops on a fiber is studied with numerical simulations. We evidence that theevaporation rate is almost independent of the wetting properties of the liquid, even for smallcontact angles, and that the droplets evaporate as spheres of the same volume.