The paper deals with the manipulator static stability analysis under the influence of the external loading. It proposes a new technique that allows evaluating both static stability of the end-effector location and static stability of the kinematic chain configuration. This approach extends the classical notion of the manipulator static stability that is completely defined by the properties of the Cartesian stiffness matrix. The advantages of the new approach are illustrated by examples that deal with parallel manipulators and their serial chains. The analysis showed that the manipulator workspace may include elastostatic singularities where the chain configurations become unstable under the influence of external loading.