The squeezing of soft solids, the constrained growth of biological tissues, and the swelling of soft
elastic solids such as gels can generate large compressive stresses at their surfaces. This causes the
otherwise smooth surface of such a solid to become unstable when its stress exceeds a critical value.
Previous analyses of the surface instability have assumed two-dimensional plane-strain conditions, but in
experiments isotropic stresses often lead to complex three-dimensional sulcification patterns. Here we
show how such diverse morphologies arise by numerically modeling the lateral compression of a rigidly
clamped elastic layer. For incompressible solids, close to the instability threshold, sulci appear as I-shaped
lines aligned orthogonally with their neighbors; at higher compressions they are Y-shaped and prefer a
hexagonal arrangement. In contrast, highly compressible solids when squeezed show only one sulcified
phase characterized by a hexagonal sulcus network.