A magnetic flux shell model is described which is suitable for numerical simulations of cylindrically symmetric plasmas. The magnetohydrodynamic equations in magnetic field line coordinates are derived including the effects of finite electrical conductivity and anisotropic heat conductivity. Subsequently, the equations of motion of coaxial plasma shells of constant density, temperature, axial velocity, and axial magnetic field are derived including (a) full radial dynamics and (b) radial pressure balance. Sample simulations of a laser heated solenoid plasma and a &Vthgr;‐pinch reactor are described.