We present a simplified description of the gravitational collapse of a uniformly rotating neutron stellar core, which can represent the final stage of the protoneutron star formed after the supernova type II explosion. The system is treated as a compressible homogeneous spheroid and the collapse time-evolution is extracted from an effective Lagrangian description of the system geometric parameters. A sudden mass quadripole change of the system at the final stage of the collapse is shown during the core bounce.