Cylinders of pure electron plasma are routinely confined within cylindrically‐symmetric Penning/Malmberg traps. When azimuthal asymmetries are imposed, the plasma deforms into appropriately asymmetric shapes. Such deformed plasmas have been observed experimentally, and are long‐lived. The equilibrium and stability of these plasmas are analyzed in this paper. A very broad class of deformed plasmas are in equilibrium, but not all such plasmas are stable. Furthermore, the flux surface adiabatic invariant assures that the plasma will attain the appropriate equilibrium shape if the azimuthal boundary perturbations are applied slowly. © 1995American Institute of Physics