It is known that by incorporating network function virtualization (NFV) in inter-datacenter (inter-DC) networks, we can use the network resources more intelligently to deploy new services faster. This paper considers an inter-DC elastic optical network (IDC-EON) and studies how to orchestrate the multicast-oriented NFV trees (M-NFV-Ts) in it efficiently. We first consider an offline scenario in which all the M-NFV-Ts are known and need to be served in the network. A mixed integer linear programming (MILP) model is formulated to solve the problem exactly, and we also propose a heuristic based on path- intersection (PI) to reduce the time complexity. With extensive simulations, we show that the proposed heuristic can approximate the MILP’s performance on low-cost M-NFV-T provisioning but only requires much shorter running time. Next, the online scenario where the M-NFV-Ts can come and leave on-the-fly is addressed, and we leverage PI to design two online algorithms for orchestrating dynamic M-NFV-Ts in IDC-EONs, i.e., with either the batch (B-PI) or sequential (S-PI) scheme. Simulation results indicate that compared with S-PI, B-PI can reduce blocking probability effectively.