A detailed numerical study of evaporating capillary jets in the Rayleigh regime is performed using a Galerkin finite-element method with penalty function formulation. The evolution of the jet surface is captured by implementing a modified form of the height flux method [1]. The evaporation rate is modeled based on the d(2) law, widely used for spherical drops. Here, the conventional d(2) law is modified by substituting the local radius of curvature of the jet surface for that of a spherical drop. The effects of the wavenumber and the initial amplitude of the surface disturbance, the Reynolds number, the evaporation rate, and the ratio of the densities of the ambient gas and the liquid are investigated. It is shown that the growth rate of the instability is enhanced and the breakup time is decreased in the presence of evaporation. The effects of evaporation on the main and satellite drop sizes are discussed and useful results are provided for variation of the drop size with various parameters. For disturbances with low wavenumber and very small initial amplitude, a sudden change in the breakup shape of the jet is observed as the evaporation rate is varied.