The result of simulation of an idealized thin wet film connecting fixed points in the Euclidean plane is a length-minimizing curve. Gradually increasing the exterior pressure we are able to achieve the film configuration near to the Steiner minimal tree. This film evolution may be an interesting tool for solving the Euclidean Steiner problem, but several dead-point situations may occur for a certain location of fixed points. A continuous evolution of the film is impossible by increasing the pressure in these situations. The investigation of dead-point situations gives the ways of overcoming the difficulties of dead-point situations and continuing the film evolution by temporarily decreasing pressure.