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The continuous tube-rolling method has been widely used to manufacture high-quality seamless pipes and tubes. However, the analytical model for determining the roll pitch diameter in three-roll continuous retained mandrel rolling from first principles has not yet been presented, which has, thus, hindered the development of rolling control technology in tube manufacturing. In this work, a new analytical model has been established from the force–equilibrium principles. The modelling has taken the tube-roll contact geometry, roll pressure, mandrel pull forces, inter-stand tensions, and friction coefficients into account for its formulations. Seen from the experimental results of the rolling at the plant, the maximum deviation of the predicted projected contact area is less than 6% and the maximum deviation of the calculated roll speed from the satisfactory data in field operation is less than 3.9%. The proposed model has enabled the influence of the friction coefficients on the roll pitch diameter to be quantified in theoretical analysis, and it was found that the changing amplitude of the theoretical roll pitch diameter corresponding to the commonly used data range of the friction coefficients can be above 9%. Having overcome the shortcomings of the empirical model, this model has the required prediction accuracy and flexibility for being applied to flexible tube rolling. By building the key algorithms around physical models, this modelling has advanced not only the rolling control at the plant, but also our scientific understanding of the mechanics of the continuous tube-rolling process.