Modeling the retention of colloidal particles in soils is important to understanding water contamination from viruses, bacteria or contaminants adsorbed on colloids. Retention by straining occurs when particles enter constrictions too narrow to permit passage. A long standing difficulty with theories of straining is a series of independent observations in which particles smaller than the smallest pore throats are nevertheless retained in a porous medium. We propose a geometric explanation for this observation, namely that particles are strained not just in throats between three grains, but also in gaps between pairs of grains. We support this explanation by characterizing such gaps in model soils (one real and many computer-generated dense packings of equal spheres, all having porosities of 34% to 36%). Of primary interest in this work are gaps having widths between 0.03 and 0.1R, R being the sphere radius. The number density of such gaps is about 0.2 per R3 bulk volume in the model soils. This is enough to trap a significant number of particles in the size range of interest (three to ten times smaller than minimum throat size). For comparison, the density of small throats (which we identify unambiguously via Delaunay tessellation of sphere centers) is about 0.3 per R3. We extend our previously established, physically representative network model to compute flow rates through the gaps. For each gap we also compute the “range of capture” for a particle of given size, i.e. the cross-section of streamlines that lead to straining that particle. Together the flow rates and geometry enable a prediction of probability of particle trapping in gaps as a function of particle size. We also obtain a conservative estimate for the volume of particles that can be trapped in gaps. The predictions are consistent with experiments, providing new insight into the mechanism of straining.