Endothelial cells, covering the inner surface of vessels and the heart, are permanently exposed to fluid flow, which affects the endothelial structure and the function. The response of endothelial cells to fluid shear stress is frequently investigated in cone–plate systems. For this type of device, we performed an analytical and numerical analysis of the steady, laminar, three‐dimensional flow of a Newtonian fluid at low Reynolds numbers. Unsteady oscillating and pulsating flow was studied numerically by taking the geometry of a corresponding experimental setup into account. Our investigation provides detailed information with regard to shear‐stress distribution at the plate as well as secondary flow. We show that: (i) there is a region on the plate where shear stress is almost constant and an analytical approach can be applied with high accuracy; (ii) detailed information about the flow in a real cone–plate device can only be obtained by numerical simulations; (iii) the pulsating flow is quasi‐stationary; and (iv) there is a time lag on the order of 10⁻³ s between cone rotation and shear stress generated on the plate. © 2005 Wiley Periodicals, Inc.