Modern browsers natively suppport file pickers that allow the user to choose multiple files at once. To activate this feature, set the multiple attribute:

<input type="file" name="images[]" multiple />

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Or in a Rails view:

<%= file_field_tag "images[]", multiple: true %>

This works in IE10+.

Make sure that the field name ends in [] so your server-side code will parse the incoming files into an array. Obviously this naming convention is not compatible with default Rails nested attribute setters, so you'll need to write a form model to adapt.