The number of Small and Medium Enterprises in Kenya have increased tremendously over the last ten years. They have played a profound role in providing employment to the population besides growing the Kenyan economy. Cloud computing is a new entrant to the technology arena which in form of Platform as a Service, Software as a Service and Infrastructure as a Service promises profound reduction in cost of operations in a business. It offers immense benefits as the business enterprise utilizes the pay per use model availed by the cloud service providers as per the needs of the business enterprise. This eliminates the need to purchase expensive software, development platforms and setting up complex ICT infrastructure. This is akin to renting what they need instead of purchasing and owning it. However, the SMEs in Kenya have not taken up the cloud computing benefits to maximise their competitive advantage. This research paper focuses on the factors that affect the adoption of cloud computing by SMEs in Kenya. The research process involves a descriptive research design. The research findings have shown that technological, organisational and environmental factors have affected the adoption of cloud technologies.