AbstractAn algorithm is given for solving minimum‐cost flow problems where the shipping cost over an arc is a convex function of the number of units shipped along that arc. This provides a unified way of looking at many seemingly unrelated problems in different areas. In particular, it is shown how problems associated with electrical networks, with increasing the capacity of a network under a fixed budget, with Laplace equations, and with the Max‐Flow Min‐Cut Theorem may all be formulated into minimum‐cost flow problems in convex‐cost networks.