A wireless 3D NoC architecture is described for building-block SiPs, in which the number of hardware components (or chips) in a package can be changed after chips have been fabricated. The architecture uses inductive-coupling links that can connect more than two examined dies without wire connections. Each chip has data transceivers for the uplink and downlink in order to communicate with its neighboring chips in the package. These chips form a vertical unidirectional ring network so as to fully exploit the flexibility of the wireless approach that enables us to add, remove, and swap the chips in the ring. To avoid protocol and structural deadlocks in the ring, we use bubble flow control, which does not rely on the conventional VC-based deadlock avoidance mechanism. In addition, we propose a bidirectional communication scheme to form a bidirectional ring network by using the inductive-coupling transceivers that can dynamically change the communication modes, such as TX, RX, and Idle modes. This paper illustrates the inductive-coupling transceiver circuits, which can carry high data transfer rates of up to 8 Gbps per channel, for the wireless 3D NoC. It also illustrates an implementation of a wireless 3D NoC that has on-chip routers and transceivers implemented with a 65 nm process in order to show the feasibility of our proposal. The vertical bubble flow control and conventional VC-based approach on the uni- and bidirectional ring networks are compared with the vertical broadcast bus in terms of throughput, hardware amount, and application performance using a full system multiprocessor simulator. The results show that the proposed bidirectional communication scheme efficiently improves application performance without adding any inductive-coupling transceivers. In addition, the proposed vertical bubble flow network outperforms the conventional VC-based approach by 7.9-12.5 percent with a 33.5 percent smaller router area for building-block SiPs connecting up to eight chips.