We perform a detailed seismic study of the beta Cep star HD 129929. Our analysis is based on the recent derivation of six pulsation frequencies. These frequencies are unambiguously identified from the seismic modelling and the photometric amplitudes to be the radial fundamental, the l = 1, p(1) triplet, two consecutive components of the l = 2, g(1) quintuplet. A non-adiabatic analysis allows us to constrain the metallicity of the star to Z is an element of [0.016; 0.022]. In addition, the fitting of three independent frequencies, two of which correspond to axisymmetric (m = 0) modes, allows us to constrain the core overshooting parameter to alpha(ov) = 0.10 +/- 0.05, as well as the other global parameters of the star. Finally, from the observation of the l = 1 triplet and part of the l = 2 quintuplet, we derive constraints on the internal rotation of this star.