Hi, we have an old brick patio in our backyard. We are thinking to replace it with concrete or paver. The
Brick patio is uneven. There is a fence with ivy around the patio. There are two
Big trees on the other side of the fence. I think one is oak, one is maple. I can see lots of roots on the ground. The contractors said they would cut the roots, and it would crack or uneven the new patio in the future. But I don't know if I should believe them. The patio will be 8 and 12 feet from the trees.

You can see some pictures at
http://www.flickr.com/photos/26094067@N07/

Thanks for any input!!

Those big ole trees could cause problems with your patio. But before you let the contractors arbitrarily cut roots it would be a good idea to get an arborist in for advice. Roots help anchor trees and if too many roots are cut from one side, the trees may not be balanced and could fall in a high wind. The trees health could also be compromised if big feeder roots are cut. Advice from someone who knows their stuff will prevent big problems from happening.

I second the emotion about the arborist. If possible to cut roots, it is possible to install root barriers to protect the new patio. The unevenness of existing patio indicates that there is already a problem with encroachment. And, keep in mind that the foundation or slab on which your structure rests is also near by and at risk.

forget the patio and have them build an elevated, but ground hugging deck.... that way, they only need to dig the footers for the posts for the deck, not much root damage, and the deck will be above the root problems.... plus the trees will be happier with it's air and water not being stopped by a patio slab kinda thing..... you can dress up a deck even nicer than a patio, too!....

Most definitely, forget the patio idea being that close to trees that most likely will cause compaction to the area under the trees.
Instead, as Toots has suggested, build a cedar decking that is raised and poses no danger of causing distress to the trees.

Your contractor undoubtedly is aware that tree roots can be safely cut outwards from the trunk when they follow certain guidelines.
Figure out for yourself and compare with what their ideas are.
Measure up the trees 4 1/2'; there measure the trees' diameter...in inches...and multiply that figure times 3 to give you the number of feet outwards that is quite safe to cut roots.

Feeder roots of trees are being cut or interfered with daily and their removal does not pose any danger to the trees' health and soon thereafter are replaced in any case.
e.g. if the diameter is 10" at 4 1/2 up...times
3, that gives a figure of 30 feet outward from the trunk it is perfectly safe to cut roots.

The distance you say the proposed patio would be--at 10 - 12 feet does suggest such removal of roots should not be attempted.
Instead, build the deck idea. It can be built with drainage of the area and the trees' continued good health in mind.
Such deck does not bring about much increase of compaction of the soil.