The acceptance factors of cloud computing in small and medium-sized companies in the service sector in Medellín (Colombia), through the Technology Acceptance Model are presented and analyzed. The methodology was exploratory and descriptive, executing the research in two steps: a literature review, followed by the application of interviews to five members belonging to organizations of the service sector. As a result, of this emerges a model of adoption of this technology, delimited by three types of variables: strategic, competitiveness and performance, showing to be useful and user friendly. Although the relation with the Cloud Computing depends upon the environment and the experiences of the small and medium-sized companies, the model contributes in different ways to technology development and to knowledge-based innovation.