Hexagonal packing geometry is a hallmark of close-packed epithelial cells in metazoans. Here, we used fiber cells of the vertebrate eye lens as a model system to determine how the membrane skeleton controls hexagonal packing of post-mitotic cells. The membrane skeleton consists of spectrin tetramers linked to actin filaments (F-actin), which are capped by tropomodulin1 (Tmod1) and stabilized by tropomyosin (TM). In mouse lenses lacking Tmod1, initial fiber cell morphogenesis is normal, but fiber cell hexagonal shapes and packing geometry are not maintained as fiber cells mature. Absence of Tmod1 leads to decreased gammaTM levels, loss of F-actin from membranes, and disrupted distribution of beta2-spectrin along fiber cell membranes. Regular interlocking membrane protrusions on fiber cells are replaced by irregularly spaced and misshapen protrusions. We conclude that Tmod1 and gammaTM regulation of F-actin stability on fiber cell membranes is critical for the long-range connectivity of the spectrin-actin network, which functions to maintain regular fiber cell hexagonal morphology and packing geometry.