The concept of flame stretch is extended to study stationary premixed flames with a finite thickness. It is shown that the analysis results in additional contributions to the stretch rate due to changes in the flame thickness and due to density variations along the flame. Extended expressions are derived that describe the effect of stretch on variations in scalar quantities, such as the enthalpy. These expressions are used to determine local variations in the flame temperature, and it is shown that known results are recovered when a number of approximations are introduced. The extended stretch formalism might be useful to analyze and quantify the different flame stretch contributions and their effects in numerical flame studies. Finally, the different contributions to the total stretch rate and the effects thereof on the flame stabilization are numerically computed for the flame tip of a two-dimensional Bunsen flame as illustration.