  The COMET experiment focuses on searching for the direct conversion of a muon
into an electron with aluminum nuclei without emitting a neutrino (so-called
$\mu\rightarrow e$ conversion). This conversion violates charged lepton flavor
conservation law, a fundamental principle in the Standard Model. The COMET
experiment requirement is to achieve the muon-to-electron conversation
sensitivity on a level of $10^{-17}$. The Straw Tracker System (STS) based on
straw tubes could provide the necessary spatial resolution of 150 $\mu$m and
the electron momentum resolution better than 200 keV/c.
  The COMET experiment will be separated into two phases. Phase-I will operate
with the 3.2 kW 8-GeV-proton beam, and Phase-II will operate with beam
intensity increased to 56 kW. STS must operate in a vacuum with 1 bar internal
pressure applied to straws. The initial design of 10-mm-diameter straws
developed for phase-I will not be as efficient with the 20 times increased beam
intensity of Phase II, but the new STS design based on 5-mm-diameter 12-$\mu$m
thick straws could fully satisfy the required efficiency. The mechanical
properties of these straws, such as sagging, elongation, dependence of the
diameter on over-pressure, etc, are discussed in this article.
