In this paper, synthesis of an arbitrary elastic behavior with an elastic mechanism is addressed. The mechanisms considered are parallel and serial mechanisms with concurrent axes. We show that any stiffness matrix can be realized through a parallel mechanism with all spring axes intersecting at a unique point. This point is shown to be the center of stiffness. We also show that any compliance matrix can be realized through a serial mechanism with all joint axes intersecting at a unique point. This point is shown to be the center of compliance. Synthesis procedures for mechanisms with these properties are provided.