Networking plays a crucial role in Cloud service delivery and network Quality of Service (QoS) has a significant impact on Cloud service performance. Cloud services for data-intensive computing applications typically require high throughput data transmission, which in some cases may not be achievable with a single end-to-end path in the network. Therefore multi-path data transmission in wide area networks for supporting Cloud service delivery is necessary. Performance evaluation on multi-path communications for Cloud service delivery is still an opening challenging issue. In this paper, we propose a novel model of networking systems for Cloud service delivery with multiple paths and develop techniques for analyzing delay and backlog performance of such systems. We employ network calculus in this paper to address some new challenges brought in by multi-path networking for Cloud service delivery. Applying network calculus makes our modeling and analysis applicable to inter-domain heterogeneous networking systems for supporting a wide variety of Cloud services. Numerical results are also given in the paper to illustrate applications of the developed modeling and analysis techniques.