The significant developments and great contributions that Cloud computing technology has achieved recently has made them widespread and the focus of attention by many of the Small and Medium Enterprises (SMEs) around the world. This has helped them to take advantage of this technology to facilitate and improve business. In the last decade, many SMEs have utilised Cloud computing technology in an effective manner and benefit from its services. This has contributed to accelerating the success and sustainability of the business sector. However, the adoption rate of Cloud computing services by Saudi SMEs is still low due to some influencing factors. This paper examines the four main influencing factors that impact on Cloud computing adoption by SMEs in Saudi Arabia which are the technological context (data confidentiality, data integrity, data security, relative advantages, service cost, and service quality), the organisational context (organisation regulations, organisation size, technology readiness, and top management support), the environmental context (technology infrastructure, Cloud provider, legal framework, and enterprise competitiveness), and the social context (culture, awareness, and trust). This paper will use both quantitative (survey) and qualitative (semi-structured interviews) methods to collect the data and evaluate the proposed model. This paper proposes a new comprehensive model called the adoption of Cloud computing model by Saudi Arabian SMEs (ACCM-SME). This was the framework created to explore the factors influencing the adoption of Cloud computing services by Saudi SMEs. Therefore, the findings of this study are aimed at contributing by increasing the Saudi SMEs' intention to adopt Cloud computing services.