AbstractStream surfaces are well‐known and widely‐used structures for 3D flow visualization. A single surface can be sufficient to represent important global flow characteristics. Unfortunately, due to the huge space of possible stream surfaces, finding the globally most representative stream surface turns out to be a hard task that is usually performed by time‐consuming manual trial and error exploration using slight modifications of seed geometries. To assist users we propose a new stream surface selection method that acts as an automatic preprocessing step before data analysis. We measure stream surface relevance by a novel surface‐based quality measure that prefers surfaces where the flow is aligned with principal curvature directions. The problem of seed structure selection can then be reduced to the computation of simple minimal paths in a weighted graph spanning the domain. We apply a simulated annealing‐based optimization method to find smooth seed curves of globally near‐optimal stream surfaces. We illustrate the effectiveness of our method on a series of synthetic and real‐world data sets.