A one-dimensional (1-D) model for thinning of the Earth's plasma sheet (Chao et al., Planet. Space Sci., vol. 25, 1977, p. 703) according to the current disruption (CD) model of auroral breakup is extended to two dimensions. A rarefaction wave, which is a signature component of the CD model, is generated with an initial disturbance. In the 1-D gas model, the rarefaction wave propagates tailward at sound velocity and is assumed to cause thinning. Extending to a two-dimensional (2-D) gas model of a simplified plasma sheet configuration, the rarefaction wave is weakened, and the thinning ceases to propagate. Extending further to a 2-D plasma model by adding magnetic field into the lobes, the rarefaction wave is quickly lost in the plasma sheet recompression, but the plasma sheet thinning is still present. It propagates at a slower velocity than a 1-D model suggests, behind a wave train of pulses of increased pressure generated by the thinning process itself. This shows that the dynamics of plasma sheet thinning may be dominated by sheet–lobe interactions that are absent from the 1-D model and may not support the behaviour assumed by the CD model.