Tim Mitchell shows us how to use the foreach loop component to iterate over a set of files:
The SSIS foreach loop is configured to allow you to easily ingest multiple data files in a single data flow task. For this to work, all of the files would need to reside in the same directory structure (either locally or on the network), and they must all have the same structure and metadata.
In this design, the data flow is contained within the foreach container, which will execute the contents of that data flow task once for each file found in the specified directory.
This gives us a good pattern for loading a bunch of text files, such as monthly extracts from a different system.