The carbon-in-pulp (CIP) process is used extensively in the mining industry to recover dissolved gold from cyanide-leached pulps. The pulp normally contains inorganic material that could penetrate the pores of the carbon. In the formulation of the model it was proposed that the loading of solid species from the hulk suspension onto activated carbon is dependent on different probabilities such as the activity of pores at the outer shell of the carbon, the concentration of fines in suspension, the stirring speed of the suspension, zeta potential of solid fines, and the fraction of fines smaller than the size of a specific pore. The proposed model was shown to describe the intrusion of solid fines in carbon accurately under a wide variety of conditions. The model was not so sensitive towards zeta potential of the solid particles or the effective stirring speed. The concentration of solid fines in the suspension influenced the collision-kinetics and hence the rate of intrusion. The concentration decay of solid fines in suspension was very sensitive at low concentrations, whereas at high concentrations the model-output concentration remained constant.