The dynamic behavior of magnetically driven axisymmetric plasma sheets of negligible thickness is examined by postulating a simplified two‐dimensional plasma sheet model. The equations of motion in the axial and radial directions are derived in Lagrangian form for the general case of time‐varying current. For the case of constant current, the general solution of the equations of motion is obtained. These equations of motion are solved for three different types of small sinusoidal perturbations of a cylindrical implosion. The plasma sheet configurations, particle trajectories, and surface mass density variations are presented for representative examples.