Within the EMI project, the European Grid Middlewares ARC, gLite, UNICORE and dCache will be improved on interoperability and made more integrated. These efforts include the communication between them, where the access to each others services is made easier and more comprehensive. In the Grid, the data are stored on storage elements of different sizes. Most of them are managed by Storage Resource Managers (SRM) and are accessible via the SRM protocol. Until now, UNICORE doesn't provide a way to use the SRM protocol, thus there is no access to SRM managed storages. To improve this situation for the UNICORE users, one task of EMI is to integrate access to these common Grid storage systems into UNICORE. This will be achieved by implementing an interface for client access to SRM storages. Additionally to SRM-based management, many files in the Grid are indexed in file catalogues, like the LHC File Catalogue (LFC), which is a part of gLite. There exist file catalogues that are VO-based, as well as for smaller user communities. If UNICORE supports access to the LFC, users may have a structured global view of their data, independent of the actual storage element where the data are stored, and can access these data. Therefore, the second Grid storage integration topic of EMI is the provision of UNICORE access to the LFC file catalogue. This paper presents which techniques are used to reach these goals, explains details of the UNICORE model of storage handling and how it is used to implement client access to SRM storand LFC. Typical file operations on SRM and LFC, necessary in the stage-in or stageout processes in UNICORE jobs are described, as well as the current implementation status, handicaps and future plans. This work was funded by the EMI project under European Commission Grant Agreement INFSO-RI-261611.