A meteor shower can be modeled, to first order, as a parallel stream of particles encountering the Earth. Gravity bends the trajectories of these particles inward, producing an increase in flux both near the planet and along the anti-radiant line. This effect is known as gravitational focusing, and the interception of a portion of meteoroid trajectories by the Earth or another massive body is known as planetary shielding. For a perfectly parallel meteoroid stream, gravitational focusing produces a flux singularity along the anti-radiant line, near which intense enhancements in flux occur. In reality, meteoroids will exhibit some dispersion in their motion that removes this singularity. We present a modified analytic treatment of gravitational focusing and planetary shielding that takes this dispersion into account and discuss its ramifications for several problems in meteor astronomy.