In this paper we present Stateless Network Functions, a new architecture for network functions virtualization, where we decouple the existing design of network functions into a stateless processing component along with a data store layer. In breaking the tight coupling, we enable a more elastic and resilient network function infrastructure. Our StatelessNF processing instances are architected around efficient pipelines utilizing DPDK for high performance network I/O, packaged as Docker containers for easy deployment, and a data store interface optimized based on the expected request patterns to efficiently access a RAMCloud-based data store. A network-wide orchestrator monitors the instances for load and failure, manages instances to scale and provide resilience, and leverages an OpenFlow-based network to direct traffic to instances. We implemented three example network functions (network address translator, firewall, and load balancer). Our evaluation shows (i) we are able to reach a throughput of 10Gbit/sec, with an added latency overhead of between 100µs and 500µs, (ii) we are able to have a failover which does not disrupt ongoing traffic, and (iii) when scaling out and scaling in we are able to match the ideal performance.