This paper presents some experimental and theoretical results for dispersion processes occurring in consolidated Berea sandstone with radial flow geometry. A comprehensive review of the derivation and application of several analytical solutions is also presented. The Galerkin finite element method is applied to solve the advection-dispersion equation for unidimensional radial flow. Individual and combined effects of mechanical dispersion and molecular diffusion are examined using velocity-dependent dispersion models. Comparison of simulated results with experimental data is made. The effect of flow rates is examined. The results suggest that a linear dispersion model, D = alpha u, where D is the dispersion coefficient, u the velocity and alpha a constant, is not a good approximation despite its wide acceptance in the literature. The most suitable mathematical formulation is given by an empirical form of D = D-o + alpha u(m), where D-o is the molecular diffusion coefficient. For the range of Peclet number (Pe = vd/D-m where v is the characteristic velocity, d the characteristic length and D-m the molecular diffusion coefficient in porous media) examined (Pe = 0.5 to 285), a power constant of m = 1.2 is obtained which agrees with the value reported by some other workers for the same regime. From the results of experiments and numerical modelling, the effect of mobility ratios (defined as the ration of viscosities of displaced and displacing fluids) on dispersion is found to be negligible, provided that the ratio is favourable.