A numerical model has been developed in this study for analysing the influence of Sips sorption isotherm on the contaminant transport mechanism in a coupled fracture matrix system. The implicit finite difference numerical technique has been used to solve the coupled non-linear governing equations. A varying grid is adopted at the fracture and rock matrix interface to capture the mass transfer at the interface. A constant continuous source of contaminants is assumed at the inlet of the fracture and the fracture is assumed to be saturated. Results suggest that the magnitude of the Sip’s equilibrium constant in the fracture is extremely sensitive in deciding the resultant transport behaviour within the high permeable fracture. The magnitude of the Sip’s model exponent within the high permeable fracture is highly sensitive in deciding the timing of zero concentration (exhaustion) within the high permeable fracture. © 2016, Korean Society of Civil Engineers and Springer-Verlag Berlin Heidelberg.