Two‐dimensional (r‐z) magnetohydrodynamic simulations of the electromagnetic implosion of metallic foil plasmas show, for certain initial configurations, a tendency to develop large‐amplitude perturbations characteristic of the hydromagnetic Rayleigh‐Taylor instability. These perturbations develop at the plasma magnetic field interface for plasma configurations where the density gradient scale length, the characteristic dimension for the instability, is short. The effects on the plasma dynamics of the implosion will be discussed for several initial foil configurations. In general, the growth rates and linear mode structure are found to be influenced by the plasma shell thickness and density gradient scale length, in agreement with theory. The most destructive modes are found to be those with wavelengths of the order of the plasma shell thickness.