We consider the problem of finding an integral multicommodity flow in a planar, undirected graph where all sources and all targets are on the boundary of the infinite face. Moreover, all capacities and all demands satisfy the so-called evenness condition. The best algorithm known so far requires ${\cal O}(kn+n^2)$ time, where n denotes the number of vertices and k the number of source—target pairs. In this paper we introduce an algorithm that is based on a completely new approach and is asymptotically optimal, that is, requires only ${\cal O}(kn)$ time in the worst case.