Estimation of separation or minor pressure losses for pipe fittings of a pneumatic conveying system at design stage is critical as much as determination of frictional pressure losses through it. The flow in many pneumatic conveying systems is a two-phase flow; it is so complex and difficult to be investigated by experimental techniques. The static pressure recovery and the minor loss coefficient through an axis-symmetric, circular cross-section, sudden-expansion fitting of a horizontal pneumatic conveying line with air-solid particle flow are analytically studied. The theoretical models proposed in the literature are scarce, and do not confirm the experimental studies. The well-known homogeneous and separated flow models proposed in the literature are initially applied to the case by means of mass and momentum conservation laws. The predictions of both the models on the pressure recovery were compared with the experimental and the numerical data in the literature and a bad agreement was observed between them; therefore, a new original analytical model is proposed by the present study. The new model is called as the slip flow model, which takes into account the slip velocity between gas and solid phases evaluated by coupling the well-known separated flow model with the empirical slip ratio predictions in the literature. The predictions of the proposed slip flow model on both the pressure recovery and minor loss coefficient are found in good agreement with the corresponding data in the literature. (c) 2008, The Society of Powder Technology Japan. Published by Elsevier BV and The Society of Powder Technology Japan. All rights reserved.