Cloud computing services are a prominent innovation that has changed consumer behaviours towards adopting new technological services. Despite the popularity of this technological innovation the underlying factors that contribute to a consumer's intention to adopt cloud computing services has not been well researched. This paper builds upon the well-known behavioural intention theories of the technology acceptance model and social cognitive theory to develop and test a number of hypotheses designed to understand the factors influencing intention to use cloud computing services. The research hypotheses in the paper propose that perceived usefulness, consumer innovation attitude, social norms, performance expectancy and trust influence behavioural intentions of consumers towards cloud computing services. The hypotheses are tested in a sample of United States and Chinese consumers to understand whether there are differences in behavioural attitudes towards technological innovations. The paper identifies research limitations, practical implications and future research suggestions.