Negative mass instability via numerical computations is investigated for the case of a cylindrical relativistic beam gyrating within two perfectly conducting cylinders concentric with the beam. The growth of the instability was followed into the nonlinear regime up to the point of saturation. The investigation show that as a result of this instability the beam breaks up into azimuthal clumps, with final field energies in radial electric field and the magnetic field produced by the beam increased by an order of magnitude over their equilibrium starting values.