From fundamental principles, the interaction of directed energetic electrons with a high-temperature hydrogenic plasma is analytically modeled. The randomizing effect of scattering off both plasma ions and electrons is treated from a unified point of view. For electron energies less than 3 MeV , electron scattering is equally important. The net effect of multiple scattering is to reduce the penetration from 0.54 to 0.41 g/cm(2) for 1 MeV electrons in a 300 g/cm(3) plasma at 5 keV . These considerations are relevant to "fast ignition" and to fuel preheat for inertial confinement fusion.