An Application Service Provider (ASP) is a company that offers individuals or enterprises access over the Internet to applications and related services that would otherwise have to be located in their own personal or enterprise computers. The simplest way to understand the ASP concept is to think of it as "application-renting". However, the customer always owns the data. The primary purpose of this thesis is to see what kind of demands there is on an ASP solution from the customers? side. The secondary purpose is to see if the customers could consider an ASP solution if their demands were met. We have also given an explanation of the ASP concept and what factors, within the data security context, makes the solution acceptable among customers. The method we have used to find a result to our hypothesis and research questions, is that we have collected different text materials and conducted interviews. The interviewed companies where four ASP suppliers and four future possible ASP customers. The result of our investigation showed that a majority of the interviewed persons could consider an ASP solution. The result could however not be estimated and applied for the entire company, because of the variety of knowledge between the different departments. The ASP industry is clearly in the stage of maturity within the IT business, but it seems like the psychological barrier may be the strongest factor that can diminish the success of ASP.