The classical result of Smoluchowski [Z. Phys. Chem.92, 129 (1917)] for the collision rate of monodisperse particles in a laminar shear flow is shown to be inaccurate due to the inclusion of the self-collision. In the present work we extend Smoluchowski’s result by excluding the self-collision in the counting of collision pairs. A numerical simulation for particle collisions in a laminar shear flow at very low concentration is carried out to validate the extended result of Smoluchowski. Good agreement for the collision rate between the numerical simulation and the prediction based on the extended expression is obtained. ©1998 American Institute of Physics.