A negative stiffness structure for vibration isolation, shock mitigation, and/or signal processing includes a flexible tensile member and a curved compressive member. A first end of the tensile member is attached to a first structure. A first end of the curved compressive member is coupled to a first structure and a second end of the curved compressive member is coupled to a second end of the flexible tensile member. A length of the tensile member is greater than a length of the compressive member. A tip of the negative stiffness structure is configured to exhibit a negative stiffness mechanical response to a load applied to the tip. The negative stiffness mechanical response acts in a direction orthogonal to the length of the tensile member.