The Functional Transformation Method (FTM) is an established method for sound synthesis by physical modeling, which has proven its feasibility so far by the application to strings and membranes. Based on integral transformations, it provides a discrete solution for continuous physical problems given in form of initialboundary-value problems. This paper extends the range of applications of the FTM to brass instruments. A full continuous physical model of the instrument, consisting of an air column, a mouthpiece and the player’s lips is introduced and solved in the discrete domain. It is shown, that the FTM is a suitable method also for sound synthesis of brass instruments.