Galgoul et al. (2004) have written a previous paper in which they have pointed out the conservatism of the latest recommendations for pipeline freespan evaluations, associated to the way the axial force is considered in the determination of the pipeline natural frequency. First because it fails to consider the fact, that the axial force of a sagging pipe, subject to temperature expansion, is much smaller than that of a straight pipe. Second because the effective axial force caused by internal pressure should not be used to determine the pipeline natural frequency. Fyrileiv and Collberg (2005) also discussed this aspect. In order to back up their previous arguments the authors decided to perform some tests an axially restrained pipeline at both ends, which was pressurized in order to justify their claims that these pipelines are not only under tension (and not compression), but also that their natural frequencies increase instead of reducing, although they do bend out because of the pressure, reaching a point of instability. The authors understand the effective axial force concept and the enormous simplifications, which it brings to an otherwise cumbersome problem, but wish to emphasize that these advantages are not unlimited and that this is one of these restrictions. To back up the text results a finite element model has been produced, in which the internal pressure is taken into account as it actually is (and not as an axial force) to show that the pipe wall stresses can only be obtained correctly in this manner.