The aim of this paper is to study by direct numerical simulation the effect of a shear-thickening behaviour of a surfactant solution, on the fluid flow, and especially on the friction coefficient in a plane channel flow. A three-dimensional model named Surfactant Drag Reduction Study (SUDRES3D) [S. Guillou, R. Makhloufi, Direct numerical simulation of an incompressible channel flow in presence of an additive, in: J. Sobota, R. Verhoeven (Eds.), Proc. 11th Intemational Conference Transport and Sedimentation of Solid Particles, AXA, Wroclam, 2002, pp. 151-1581 was developed to apply to DNS. The shear-thickening theological behaviour of an aqueous surfactant solution (Ethoquad O/12 (500 ppm) + NaSal (330 ppm)), studied previously by Usui et al. [H. Usui, T. Itoh, T. Saeki, On pipe diameter effects in surfactant drag-reducing pipe flows, Rheol. Acta 37 (1998) 122-128], is modelled here by a combination of two shear-thinning CarTeau laws, which is later referred to as composed law. The calculations are performed first separately with the two shear-thinning Carreau laws and the composed law for different Reynolds numbers either in laminar and turbulent flows. The results are compared between them. It appears that for the set of parameters used, corresponding to the experimental data, the shear-thickening has no major effect on the wall friction and then no Drag Reduction occurs. Secondly, some calculations are performed with a chosen set of parameters. They show that such kind of behaviour may have a positive effect on the friction coefficient and a drag reduction phenomenon appears, but under restrictive conditions. (D 2007 Elsevier B.V. All rights reserved.