A manifold structure and method of forming a manifold structure includes using an ultrasonic additive manufacturing (UAM) process to build up a solid structure, machining the solid structure to form a cavity and free-standing support pillars within the cavity, and using a UAM process to build up a finstock layer over the cavity. The support pillars formed by machining have yield strengths high enough to support UAM of the finstock layer over the cavity. A plurality of finstock layers are built up within the cavity to segment the cavity into a plurality of cavities. UAM of the finstock layers enables the finstock layers to be stacked in a direction normal to a direction of flow through the cavity for efficiently transferring heat through the manifold structure.