Hi cindyforstan,
Currently, the feature “Upload Multiple Documents” isn’t supported on the computers without Internet Explorer.
Instead, you can use Microsoft Document Connection to upload multiple files as mchv2.0 suggested above.
In addition, you can refer to the article below for more information:
blogs.msdn.com/.../sharepoint-2010-on-a-mac-with-office-for-mac-2011.aspx
Thanks,
Nancy Xie