This paper presents a new numerical method, the finite cell method (FCM), for simulating complex biological and chemical transport phenomena in porous media. It has the same advantages as the random walk method (RWM): there is no advection-dispersion equation to be solved, it is unnecessary to calculate the concentration distribution in each time step, and there is no numerical dispersion for the case of high Peclet number. The concept of FCM, however, is different from the RWM in several aspects. The minimum unit in the FCM is a cell that has a certain volume and carries variable mass, while in the RWM the minimum unit is a particle that has no volume but carries a certain mass. In the FCM we use multiple sets of cells to represent different phases in a porous medium. A mobile or an immobile cell may carry multiple biological and/or chemical components. Mass exchanges may occur not only between cells but also within cells. These mass exchanges can be described by different rules: equilibrium or nonequilibrium, linear or nonlinear. In this paper, a one-dimensional FCM code is developed and used to simulate the solute transport with nonequilibrium adsorption, colloid transport with kinetic deposition and release, and colloid facilitated transport with kinetic mass exchanges. The FCM solutions have been compared with available analytical solutions and the solutions obtained by the finite difference method (FDM). Results show that both FCM and FDM solutions match analytical solutions quite well when the concentration front is flat. When the concentration front is sharp, however, the FDM solutions become inaccurate because of numerical dispersion, but the FCM can still produce very accurate peak and tailing concentrations. From the example of colloid-facilitated transport, we can see how a complex chemical and biological transport procedure in porous media can be simulated directly by the FCM without solving any advection-dispersion equation. ¿ 1999 American Geophysical Union