A modal computation of a complete clarinet is presented by the association of finite-element models of the reed and of part of the pipe, and a lumped-element model of the rest of the pipe. This is a continuation of an initial work by Pinard and Laine (unpublished reports of the Ecole Polytechnique) on isolated reeds. The eigenmodes of the complete system are computed and the results lead to a discussion of the following points: flexion and torsion modes of the reed, their coupling to the acoustical field, plane wave hypothesis, equivalent volume approximation in the mouthpiece, and alignment of resonance peaks.