In the biomechanics field, tensegrity structures are considered to be similar to the human skeleton and the joint. Oh proposed a bio-tensegrity model that mimics the human spine and presented a shape control strategy, which leads to the optimization problem with the lengths of the tensile members corresponding to the muscle and tendon as design variables. It has been pointed out that this model has low initial stiffness and buckling occurs during shape control to avoid obstacles. In this study, a method for modifying the shape and self-equilibrium stress so that the minimum eigenvalue of the stiffness matrix in the initial state becomes the specified value is presented. Furthermore, with constraints on the eigenvalues of the tangent stiffness matrix, we extend to a shape control method that avoids obstacles without buckling.