The limit analysis informs us of the allowance ranged from the incipient yielding to the rupture of a pressure vessel providing the limiting load and the corresponding collapse mode. A general algorithm developed for limit solutions calculates the collapse load of a thick-walled tube under internal pressure and demonstrates its validity as compared with various solution methods. The collapse load of a tube varies significantly with the amount of defect on a tube. The collapse load decreases very slowly with the small amount of defect and rapidly with the large amount of defect. The corresponding collapse modes change unexpectedly and interestingly from the normal mode without defect.