Log into your Blackboard course and go the Control Panel:

1. Click on Grade Center.
2. Select Full Grade Center.

Click the chevron in the column header of the assignment column and choose Assignment File Download

You will now see a screen labeled Download Assignment:

1. Check the boxes next to the names of the students whose submissions you want to download. To select all students on the page, check the checkbox at the top of the page. 
2. To see all students, click the Show All button at the bottom of the screen.
3. Select Files: Choose either to download the last attempt file or all attempt files. (This option will only appear if the assignment is set to allow multiple submissions and at least one student has submitted more than one attempt)
4. When finished, click the Submit button.

Blackboard will now inform you that the selected files have been packaged, and you will be provided a link to download the file to your computer.  Click on the link, and your browser will ask you where to save your file.