The German-Russian Astroparticle Data Life Cycle Initiative is an international project launched in 2018. The Initiative aims to develop technologies that provide a unified approach to data management, as well as to demonstrate their applicability on the example of two large astrophysical experiments - KASCADE and TAIGA. One of the key points of the project is the development of a distributed storage, which, on the one hand, will allow data of several experiments to be combined into a single repository with unified interface, and on the other hand, will provide data to all participants of experimental groups for multi-messenger analysis. Our approach to storage design is based on the single write-multiple read (SWMR) model for accessing raw or centrally processed data for further analysis. The main feature of the distributed storage is the ability to extract data either as a collection of files or as aggregated events from different sources. In the last case the storage provides users with a special service that aggregates data from different storages into a single sample. Thanks to this feature, multi-messenger methods used for more sophisticated data exploration can be applied. Users can use both Web-interface and Application Programming Interface (API) for accessing the storage. In this paper we describe the architecture of a distributed data storage for astroparticle physics and discuss the current status of our work.