How do I delete several messages at a time

Highlight one then hold CMD key wilst clicking on others you want to delete, then Delete.

The advice from BDAqua works just fine on individual messages within a message thread or conversation.

If you're trying to delete more than one entire thread or conversation at a time, there is not a way to do that, unfortunately.

Doesn't work. When I hold down the command key and click on another message, the first message deselects.

Same here, neither the command key or the shift key works. I can only select one message at a time, if I attempt more it deselects the first message and so on.