We study the boson peak phenomenology experimentally observed in globular proteins by means of elastic network models. These models are suitable for an analytic treatment in the framework of Euclidean random matrix theory, whose predictions can be numerically tested oil real protein structures. We find that the emergence of the boson peak is strictly related to an intrinsic mechanical instability of the protein. in close similarity to what is thought to happen in glasses. The biological implications, Of this Conclusion are also discussed by focusing Oil a representation case study.