A simple, analytic approximate theory has been developed for calculation of x-ray transport in one-dimensional Cartesian geometry. The form of the theory is particularly suited to numerical computation. Deposition and energy currents can be calculated in times comparable to those required by exponential mass-absorp-tion codes, with accuracies comparing favorably with more sophisticated discrete ordinates or Monte Carlo calculations. Although the theory is presented in terms of x-ray transport, it should be applicable to any transport problem for which (a) scattering is not highly anisotropic, and (b) averaged cross sections may be defined for secondary particles.