  We have numerically solved the Grad-Shafranov equation for axisymmetric
static MHD equilibria of matter confined at the polar cap of neutron stars.
From the equilibrium solutions we explore the stability of the accretion mounds
using the PLUTO MHD code. We find that pressure driven modes disrupt the
equilibria beyond a threshold mound mass, forming dynamic structures, as matter
spreads over the neutron star surface. Our results show that local variation of
magnetic field will significantly affect the shape and nature of the cyclotron
features observed in the spectra of High Mass X-ray Binaries.
