Analytical solutions of differential equations applicable to extraction, ion exchange, or adsorption processes in packed beds are presented. Results are given for three different cases. The first case accounts for adsorption phenomena only. The second one includes surface adsorption on particles and the effects of longitudinal dispersion in the bed. The third one deals with diffusion in particles and longitudinal dispersion in the bed. In the mathematical modelling of these three cases, a linear equilibrium relationship between the solute in the liquid phase and solute in the solid phase is used. The first case is solved using the single boundary condition at the feed end of the column. In the second case, two different sets of boundary conditions are used. One set uses two conditions at the feed end: namely, the feed composition and its variation with respect to length. The other set uses an equation of continuity at the inlet of the column, and solute material balance over the entire column. In the third case, the feed composition is one boundary condition, while the other assumes a linear concentration profile at the-discharge end of the column. Since the boundary conditions involving the mass conservation law and the highest derivative of the differential equations are beyond the criterion which are found in the literature, the applications of boundary conditions for solving differential equations are extended. Comparisons are made with previous models and experimental data in the literature.