The solution of a Boltzmann equation for electron transport is discussed with emphasis on its application to x‐ray production and electron scattering in electron‐probe microanalysis. Particular attention is given to the assumptions involved in associating an energy, a cross section for scattering, and a cross section for ionization with each position along the electron path. The Spencer‐Fano theory of electron stopping power is applied. The treatment of electron scattering of Brown and Ogilvie is refined using (1) a single scattering equation for short path lengths, (2) a transport equation for intermediate path lengths, and (3) a diffusion equation for long path lengths. The predictions of this Transport Equation Program are compared with experimental data for (1) the energy distribution of backscattered electrons, (2) the depth distribution of x‐ray production, and (3) x‐ray intensity ratio as a function of alloy composition. The x‐ray intensity ratios are corrected for fluorescence due to the continuum, and it is indicated that this correction may be significant.