This study is concerned with the effects of surface tension on the steady potential flow of a liquid issuing from a two‐dimensional slot with inclined walls. The mathematical problem, which is characterized by a nonlinear boundary condition along the free streamline, is solved using a novel numerical technique based on the fast direct Poisson solver. Numerical solutions were obtained for various Weber numbers and slot angles, and the results are compared with the free streamline shapes and contraction coefficients of the corresponding classical potential solutions without surface tension, and with some available theoretical results. When the numerical grid size is reduced or when the Weber number is sufficiently small, undesirable standing waves appear on the free surface that violate a causality condition. The cause of these waves was examined. A criterion was found for the occurrence of the waves.