Modes oscillating at the acoustic frequency and identified as beta Alfvén eigenmodes (BAEs) have been observed in Tore-Supra under ion cyclotron resonant heating. In this paper, the linear excitation threshold of these modes, thought to be driven by suprathermal ions, is calculated and compared with Tore-Supra observations. Similar studies of the linear excitation threshold of energetic particles driven modes were carried out previously for toroidal Alfvén eigenmodes or fishbones. In the case of BAEs, the main point is to understand whether the energetic particle drive is able to exceed ion Landau damping, which is expected to be important in the acoustic frequency range. For this, the BAE dispersion relation is computed and simplified in order to derive a tractable excitation criterion suitable for comparison with experiments. The observation of BAEs in Tore-Supra is found to be in agreement with the calculated criterion and confirms the possibility to trigger these modes in the presence of ion Landau damping. Moreover, the conducted analysis clearly puts forward the role of the global tunable parameters which play a role in the BAE excitation (the magnetic field, the density etc), as well as the role of some plasma profiles. In particular, the outcome of a modification of the shear or of the heating localization is found to be non-negligible and it is discussed in the paper.