Service-Oriented Computing (SOC) is emerging as a promising paradigm for developing distributed enterprise applications. Although some initial concepts of SOC have been investigated in the research literature, and related technologies are in the process of adoption by an increasing number of enterprises, the ability to measure the structural attributes of service-oriented designs thus predicting the quality of the final software product does not currently exist. Therefore, this paper proposes a set of metrics for quantifying the structural coupling of design artefacts in service-oriented systems. The metrics, which are validated against previously established properties of coupling, are intended to predict the quality characteristic of maintainability of service-oriented software. This is expected to benefit both research and industrial communities as existing object-oriented and procedural metrics are not readily applicable to the implementation of service-oriented systems.