My outside water meter is covered with water. We have had a lot of rain and I think the soil is not draining from the box. Is the water going to damage the meter?

The water shouldn't hurt. Plus the meter belongs to the water company.

That is a very common occurrence. It won't damage the meter. You just want to double check - and check the meter box after the rain season is over just to make sure the meter unions are not leaking

Milo