Abstract-This paper provides a reliable dielectric measurement theory of the open resonator for non-planar objects such as convexconcave objects. It is the first time that the complete analytical formulas of the complex permittivity are presented by means of the second-order theory of the open resonator and field matching method. Furthermore, a measurement system is designed and built at Ka band, and the consistency of the results between planar and nonplanar samples verifies the accuracy of the new theory. Finally, the experimental error analysis is investigated.