The calculation of the liberation spectrum in the product from continuous milling operations is a problem of considerable importance, and it is difficult to solve because the population balance equation must be integrated in two-dimensional space. Complete solutions require a very detailed knowledge of the complex interactions between the fracture patterns and the mineralogical ore texture when brittle particles are subject to impact fracture. Most of the liberation models that have been developed to date apply only to batch comminution processes and under these conditions the liberation problem can be studied in isolation. When the comminution is continuous and forms a unit operation in a flowsheet that includes classification and separation operations, the situation is very different, and then the liberation of the minerals must be described when single particles of known mineralogical composition are fractured. Important industrial examples are conventional milling circuits closed by hydrocyclone and regrind mills in flotation plants. This paper presents an efficient computational algorithm for the calculation of the liberation spectrum produced by continuous milling operations. The algorithm relies heavily on the detailed internal structure of the Andrews-Mika diagram. The modifications that are required to make this diagram apply to practical ore minerals, and the internal structure of this diagram can be established using single-particle fracture on mono-size, mono-grade material but suitable liberation models are essential to interpret the data in terms of the cross transfer coefficients required for the population balance procedure. Models proposed by Leroux (1992) and King (1990) are compared to experimental data.