Elasticity can be seen as the ability of a system to increase or decrease the computing resources allocated in a dynamic and on demand way. It is an important feature provided by cloud computing, that has been widely used in web applications and is also gaining attention in the scientific community. Considering the possibilities of using elasticity in this context, a question arises: “Are the available public cloud solutions suitable to provide elasticity to scientific applications?” To answer the question, in a first moment we present a survey on the use of cloud computing in scientific scenarios, providing an overview of the subject. Next, we describe the elasticity mechanisms offered by major public cloud providers and analyzes the limitations of the solutions in providing elasticity for scientific applications. As the main contribution of the article, we also present an analysis over some initiatives that are being developed to overcome the current challenges. In our opinion, current computational clouds are developing rapidly but have not yet reached the necessary maturity level to meet all scientific applications elasticity requirements. We expect that in the coming years the efforts being taken by numerous researchers in this area identify and address these challenges and lead to better and more mature technologies that will improve cloud computing practices.