This article presents a stability analysis of object grasping with a compliant multi-fingered robot hand considering the influence of the flexibility of the grasped object on this stability. In this stability analysis we aimed to compute the maximum disturbance that can be withstood by a compliant hand-object system before being destabilized. Here, the case of objects with a compliant behavior that can be synthesized in a stiffness matrix is addressed. The specific example of beam objects and cylindrical grasps is investigated, a computation of the local stiffness matrix of the beam object is proposed using Euler-Bernoulli theory for beam deflection and the influence of the Young modulus of the beam on the stability is evaluated.