The flipping motion of a blood platelet convected under the action of a simple shear flow over a substrate is discussed. The platelet is modelled as a rigid oblate spheroid with aspect ratio equal to 0.25 whose axis of revolution is perpendicular to the vorticity of the simple shear flow. The particle motion from a given initial position is computed using a boundary element method for Stokes flow based on the double-layer representation. When the platelet is far from the wall, the motion is described by Jeffery's exact solution. As the platelet approaches the wall, the rate of rotation is reduced significantly when the platelet mid-plane is parallel to wall, and mildly when the mid-plane is perpendicular to the wall. Comparison with laboratory data indicates that wall effects alone do not explain the observed slow rate of rotation. It is proposed that a distributed adhesion force imparts to the particle an effective external force and torque at the nominal point of contact, and these slow down the rate of rotation. The process is demonstrated by computing the motion of an adhering platelet whose lowest point is immobilized under the action of a suitable force and torque.