A real-time synthesis model of wind instruments sounds, based upon a classical physical model, is presented. The physical model describes the nonlinear coupling between the resonator and the excitor through the Bernoulli equation. While most synthesis methods use wave variables and their sampled equivalent in order to describe the resonator of the instrument, the synthesis model presented here uses sampled versions of the physical variables all along the synthesis process, and hence constitutes a straightforward digital transposition of each part of the physical model. Moreover, the resolution scheme of the problem ͑i.e., the synthesis algorithm͒ is explicit and all the parameters of the algorithm are expressed analytically as functions of the physical and the control parameters.