A general expression for the uptake of organic solutes from aqueous solutions by soil and sediment pellets in the Laplace domain is presented. This expression, together with the appropriate macroscopic conservation equation and initial and boundary conditions, provides a complete description of the movement and distribution of organic solutes through soil and subsurface systems. To obtain the numerical results for a specific system, the inversion from the Laplace domain into the time domain is required. In the present work, the use of two techniques, the fast Fourier transforms (FFT) and the Fourier series approximation (FSA), for inverting the Laplace transforms in connection with several problems concerning organic solute uptake by soils was explored. The FSA technique was found successful in all cases while the results by the FFT technique were strongly influenced by the selection of the algorithm parameters, In comparison with several numerical techniques for the direct solution of intraparticle diffusion equations, the FSA technique was found to have advantages in both accuracy and computational efficiency.