Internal instability is a form of internal erosion in broadly graded cohesionless soils in which fine particles can be eroded at lower hydraulic gradients than predicted by classical theory for piping or heave. A key mechanism enabling internal instability is the formation of a stress-transmitting matrix dominated by the coarse particles, which leaves the finer particles under lower effective stress. In this study, discrete element modeling is used to analyze the fabric and effective stress distribution within idealized gap-graded samples with varying potential for internal stability. The reduction in stress within the finer fraction of the materials is directly quantified from grain-scale data. The particle-size distribution, percentage finer fraction, and relative density are found to influence the stress distribution. In particular, effective stress transfer within a critical finer fraction between 24 and 35% is shown to be highly sensitive to relative density.