Recently, F,rec et al. (2009a) proposed a model for nondilute rod-like suspensions, where particle interactions are taking into account via a micromechanical approach. The derived governing equation used the well-known second- and fourth-order orientation tensors (a (2) and a (4) ) and novel second- and fourth-order interaction tensors (b (2) and b (4) ). To completely close the model, it is necessary to express a (4) , b (2) , and b (4) in terms of a (2) . This paper gives the general framework to elaborate these new relations. Firstly, approximations for b (2) are developed based on linear combinations of a (2) and a (4) . Moreover, a new closure approximation is also derived for b (4) , based on the orthotropic fitted closure approach. Unknown parameters are determined by a least-square fitting technique with assumed exact solutions constructed from the probability distribution function (PDF). As numerical solutions for the PDF are difficult to obtain given the nonlinearity of the problem, a combination of steady state solutions is used to generate PDF designed to cover uniformly the entire domain of possible orientations. All these proposed approximations are tested against the particle-based simulations in a variety of flow fields. Improvements of the different approximations are observed, and the couple iORW-CO4P3 gives efficient results.