Multiple-speed centrifuge measurement is a standard technique for obtaining the compressive yield stress of concentrated suspensions. Converting the centrifuge data into a compressive yield stress vs. volume fraction curve is an inverse problem. The problem is ill posed in the sense that noise in the data is likely to be amplified if inappropriate data processing methods are used. A method based on Tikhonov regularization is applied to solve this inverse problem. An added complication of centrifuge measurement is the interface between the uncompressed and compressed layers in the centrifuge tube. This interface is not measured and has to be treated as a free boundary. A computation scheme for locating this free boundary is incorporated into the Tikhonov regularization procedure. This new way of processing centrifuge data is assessed by applying it to synthetic data and to laboratory, data. Problems caused by small or noisy data sets are discussed.