ESDU 77016 compares seven recognised prediction methods for vertically upwards flow with a very large range of experimental results taken from the literature. By means of a statistical analysis, performance charts are developed that show for a number of ranges of both liquid volume fraction and mass velocity the order of ranking of the prediction methods in terms of accuracy and the likely errors involved for each method within those conditions. Two sets of charts are developed; one using only data for steam/water mixtures and one using all other available data. The methods are Lockhart and Martinelli, Premoli et al, Zuber, Hughmark, Armand, Chisholm, and simple homogeneous theory. From the performance charts the best prediction method can be selected and the accuracy of its prediction assessed. In addition a method is given for dealing with both upwards and downwards flow in inclined tubes by using a modified value of the mean density in conjunction with one of the vertical flow prediction methods. ESDU 76018 deals similarly with the prediction of the frictional component, ESDU 78001 gives a method for the momentum component, and ESDU 78018 shows how the methods are applied in a practical case.