The elastic should never, ever be on the side that you regularly tighten. It would make it too easy to over-tighten and severly restric the horse. The whole point of an elesticated girth is that there is 'give' when needed ie, over a fence, flat work etc. If this option of 'give' is removed by using the elastic on the wrong side then there is no point what-so-ever in choosing to use an elasticated girth.