We develop the application of age, period and cohort models to the representation of tables of age- and period-specific rates. A derivation is given by way of a familiar graphical technique. The identifiability problem is discussed, identification techniques are reviewed and a new approach is recommended that is based upon the success of the three two-variable submodels. Other constraints are introduced that enhance interpretation. Examples are given for two sites of cancer. This approach is contrasted with other methods designed to demonstrate trends. Finally, standard errors of the parameters and tests of goodness of fit are discussed.