The motion of a linear pinch due to finite axisymmetric disturbances is studied. The plasma is considered as a single, inviscid, perfectly conducting, compressible fluid, and the usual magneto-hydrodynamic assumptions are made. Theory of characteristics is applied to study simple waves. A compression simple wave is found to steepen with time and is expected to develop into a shock with area change. It is found that the increase of entropy across such a shock is greater than that across an ordinary normal shock with the same pressure ratio. With respect to a single finite axisymmetric concave or convex disturbance with small area gradient in the axial direction, the pinch is stable in the sense that it will nowhere touch the coaxial wall and its physical quantities will remain finite.

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