We employ a fiber-level simulation technique to simulate carbon nanotube (CNT)/polymer composites in simple shear flow. This model incorporates CNT flexibility, irregular CNT equilibrium shapes and CNT interactions. Electrical conductivity of the composites is determined using a resistor network algorithm. Tunneling resistance of the insulating matrix film between nanotubes is also considered. We show that the rate of imposed shear flow influences the composite conductivity by facilitating the formation or destruction of the conductive aggregates. In addition, the conductivity evolution during shearing for different concentrations is investigated. At low concentration, percolating clusters form and break simultaneously which causes large conductivity fluctuations during the simulations. When sufficiently large concentrations are reached, percolating clusters persist during shearing and the conductivity fluctuations decrease. In agreement with previous research we determine that increasing the shear rate causes alignment of the nanotubes in the flow direction. We show that upon shearing at constant shear rate, the system attains a state with substantially constant electrical conductivity, nanotube orientation and agglomerate size that is a function of the applied shear rate. The state reached for a given shear rate is independent of the initial state of orientation and aggregation. (C) 2011 Elsevier Ltd. All rights reserved.