Nowadays, service providers offer a lot of IT services in the public or private cloud. Clients can buy various kinds of services, such as SaaS, PaaS, etc. Recently, Backup as a Service (BaaS), a variety of SaaS, was introduced there. At the moment, there are several different BaaS’s available to archive data in the cloud, but they provide only a basic level of service quality. In this paper, we propose a model which ensures QoS for BaaS and some methods for management of storage resources aimed at achieving the required SLA.This model introduces a set of parameters responsible for an SLA level which can be offered at the basic or higher level of quality. The storage systems (typically HSM), which are distributed between several Data Centers, are built based on disk arrays, VTL’s, and tape libraries. The RSMM model does not assume bandwidth reservation or control, but rather is focused on management of storage resources.