In addition to the wireless network providers’ need for traffic classification, the need is more and more common in the Cloud Computing environment. A data center hosting Cloud Computing services needs to apply priority policies and Service Level Agreement (SLA) rules at the edge of its network. Overwhelming requirements about user privacy protection and the trend of IPv6 adoption will contribute to the significant growth of encrypted Cloud Computing traffic. This report presents experiments focusing on application of data mining based Internet traffic classification methods to classify encrypted Cloud Computing service traffic. By combining TCP session level attributes, client and host connection patterns and Cloud Computing service Message Exchange Patterns (MEP), the best method identified in this report yields 89% overall accuracy. / text