Additively manufactured cellular structures offer opportunities to tailor structural response while reducing material use. This study experimentally examines the tensile behavior of hexagonal cellular structures fabricated from polylactic acid (PLA) by fused deposition modeling (FDM). A full factorial design combined four nominal cell sizes (2, 3, 4, and 5 mm) with six wall thicknesses (0.5–1.5 mm), yielding 24 configurations. One specimen was tested for each configuration. Peak and fracture forces, corresponding reference stresses, effective moduli reported by the testing-machine software, and macroscopic fracture patterns were compared. Increasing wall thickness generally increased load-bearing capacity, although non-monotonic responses occurred in several configurations. The highest peak and fracture stresses were 31.09 and 28.69 MPa, respectively, for the 2 mm cell size and 1.5 mm wall thickness. The highest reported effective modulus was 1924.45 MPa for the 5 mm cell size and 1.5 mm wall thickness. Thus, the configurations associated with the highest strength and highest reported modulus differed. Fracture was observed near the solid-to-cellular transition and within the cellular region.