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A semianalytical technique to study the charged-particle transport in one-dimensional finite media is developed. For this purpose, the transport equation is written in the form of coupled integral equations, separating the spatial and energy-angle transmissions. Legendre polynomial representation for the source, flux, and scattering kernel are used to solve the equations. For evaluation of the spatial transmission, discrete ordinate representation in space, energy, and direction cosine is used for the particle and source flux. The integral equations are then solved by the fast iteration technique. The computer code CHASFIT, written on the basis of the above formulation, is described. The fast convergence of the iteration process which is characteristic of charged-particle transport is demonstrated. Convergence studies are carried out with a number of mesh points and polynomial approximations. The method is applied to study the depth-dose distributions due to 140-, 200-, 300-, 400-, 600-, and 740-MeV protons incident normally on a 30-cm-thick tissue slab. The values of the quality factor at the surface and at 5 cm depth, as well as the total average quality factor, are calculated. The results thus obtained are compared with those predicted by the Monte Carlo method. This method can also be applied to multienergy, multiregion systems with arbitrary degree of anisotropy.