There's always so much confusion about mailing square invitations and whether or not they cost more to mail. Square envelopes do cost more to mail because Canada Post go by what it's called the aspect ratio. If your invitation is not 1.3 - 2.6 : 1, then you will have to pay for non-standard shipping, which is now $1.15.
Many people look at the sizing chart of Canada Post and think that as long as the measurements fall between 140mm-245mm in length and 90mm-156mm in width and the thickness is between 0.18mm and 5mm, it takes regular postage. However, that is not the case. The chart is just to say that they will mail it, anything outside of it will be refused. It doesn't say anything about the pricing being the same or different.
Some brides would take their invitations to the post office to ask them how much it would cost to mail them. Some clerks would tell them they only have to pay regular postage. But be very careful, the clerk is wrong and chances are the invitations will be returned to you. No matter how sure the clerk is, do not take the risk! I've heard this happen to a bride before. So to avoid the invitations not getting to your guests, pay more for square envelopes.