Modelling the sedimentation of suspensions with partial differential equations requires constitutive relations (material properties) to be known. Restricted to suspensions obeying Kynch's assumption (ideal suspensions), this paper deals with the inverse problem, which is to estimate the batch-settling flux function from experimental data. A new batch-settling test is suggested, from which it is theoretically possible to estimate a large part of the flux function for lower concentrations containing the extreme point. From a standard batch-settling test, a large part of the flux function for higher concentrations can be estimated with the famous method by Kynch. For these two parts, simple general explicit formulae are derived, which contain only the initial concentration and height variables, the interface height and its derivative as a function of time. The method is demonstrated on synthetic and experimental data. Further experimental development of the new test is required. The aim of the paper is to present a theoretical foundation for the method, including the explicit formulae as a solution of the inverse problem. (C) 2007 Elsevier Ltd. All rights reserved.