The problem of determining the orientation distribution function of rigid particles of arbitrary shape is formulated in a general stochastic approach to consider any acting orientation mechanism, stochastic or deterministic. The effect of the various orientation mechanisms on the partial differential equation of the problem is analysed. A particular orientation mechanism acting on rigid ellipsoidal macromolecules in addition to the hydrodynamic and the Brownian effects is considered in Couette flow: a force field in the radial directionx, varying linearly withx. It is shown that the effect of a uniform electric field in the radial direction on polarizable ellipsoidal particles is of this nature. The corresponding steady‐state orientation distribution function is determined to the third order for the case of predominant Brownian influence, and the theory of streaming birefringence of a dilute suspension of rigid ellipsoidal macromolecules in Couette flow is generalised to include the influence of the additional orientation mechanism: the direction of the isocline and the amount of birefringence are calculated to the second order.