The aim of this paper is to establish a methodology for determining the stability area of bird postural equilibrium. The bird model presented in [1] shows that a passive tensegrity system can explain the postural equilibrium of birds, which is a key for future robotic application. The goal now is to understand the response to perturbations and the basin of attraction of this system. The stability of an equilibrium posture can be studied via the evolution of the total energy around this equilibrium. Since the system is passive, if a motion starts at a given energy level, it will remain within the region defined by that level, with the energy decreasing due to dissipation. However, due to certain constraints, the system may fall even though it should tend towards a stable equilibrium. In this paper, the existing constraints will be clarified. The basin of attraction will be defined for a simplified one-joint system, degenerating from the multibody system of bird leg. We will then validate our results using a biomechanics software, Artisynth, and experimental setup.