This paper proposes a novel Secure Multi- Geocasting Spray And Flood technique for opportunistic networks called SMGSAF, which uses secret sharing and disjoint path routing to secure the privacy of messages. In multi-geocasting, routing aims to successfully deliver a given geomessage to all the nodes, or to as many as possible, located inside defined geographic areas within a given time interval. It is desired that as long as a message is outside its destination casts it cannot be read by intermediate nodes. Encryption is a proven way to ensure this but classical encryption techniques are not well suited for the opportunistic paradigm. Key distribution and scarcity of resources are the major challenges in this regard. Therefore we have used secret sharing and disjoint path routing to protect the privacy of messages. Simulation results show that the proposed SMGSAF protocol provides the intended security but at the expense of performance, that is within acceptable limits. Notably, the SMGSAF protocol outperforms unitary geocasting in terms of delivery probability. The proposed protocol is evaluated in terms of delivery probability, network overhead, and latency. Its performance has been compared to MGSAF and GSAF.