A method for transportation of metric between simply-connected surfaces with boundary is presented. The method is based on classical uniformization and optimal mass transportation. One application of the method is a novel definition of distance function between simply-connected surfaces with boundaries. The new distance forms a tractable/constructive alternative to the theoretically sound but hard to compute Gromov-Hausdorff distance. We will also show how this distance can be used to find automatic correspondences between some "real-life" surfaces.