Displacement-length relationships of faults reveal their growth patterns with implications for the shear strength of their host rocks. This principle can be used to analyze graben on the Moon, which are composed of two down-dropped blocks of rock bounded by two antithetic normal faults. Linear elastic fracture mechanics (LEFM) and post-yield fracture mechanics models (PYFM) were used to investigate the relationship between fault growth patterns and host rock shear strength. Lunar Reconnaissance Orbiter wide-angle camera global image mosaics (100 mpp) were used to map a total of 1750 individual fault segments across the lunar surface. To better understand normal fault growth on the Moon we analyzed 14 segmented graben with 184 individual fault segments in detail. Slip distribution profiles were derived from 512ppd Lunar Orbiter Laser Altimeter digital elevation models by measuring the fault displacement along each of the investigated fault segments. These profiles reveal not only the maximum displacement, shape, and growth patterns of the individual faults, but also possible interaction with neighboring faults. LEFM and PYFM models predict idealized (elliptical) slip distribution profiles based on local stress fields and rock parameters. These modeled profiles can then be compared to our observed slip distributions. For the LEFM approach the observed fault length, and values for shear modulus and Poisson’s ratio, produced displacement shapes by only varying the remote stress that is necessary to propagate the fault. The PYFM approach considers the yield strength of the material and allows us to distinguish between zones of inelastic and elastic deformation at the fault, generating a more complex displacement profile model. The comparison between modeled and observed profiles enabled us to analyze the stress evolution on the faults with implications for the strength of the faults over time. Our findings indicate that two different fault growth trends can be observed for graben-bounding normal faults on the Moon. One set of faults likely grew with constant remote stress and yield strength, whereas the other set of faults shows that both boundary conditions decrease over time. Future analysis will reveal how properties of the host rock and frictional properties of the fault zones evolve as the structures grow larger.