A discrete two-dimensional model of a ferroelastic lattice has been employed to study the equilibrium shapes of needle domains at different depths below the surface. We have found that the trajectory of the needle tip follows the theoretically predicted form of a quadratic function. A high-symmetry high-temperature region is identified, extending from the tip of a needle below the surface, and created as a result of elastic interaction between the needle tip and the surface, giving rise to possible unexpected surface topographies. A configuration where the needle tip touches the surface initially, is found to evolve into two kinked domain walls that move away from each other.