The Steiner problem asks for the shortest network that spans a given set of fixed points in the Euclidean plane. The problem is NP hard.

The result of simulation of an idealized “wet” film connecting fixed points is a length-minimizing curve. Increasing the exterior pressure step by step we are able to achieve the film configuration near to the Steiner minimal tree. “Dead-point” situations may occur for some symmetric allocation of fixed points.

The limited simulation experiments show that the average computation time depends almost linearly on the number of fixed points for the situations without “dead-points”.