There are many rules governing Olympic rifles. Think of these when you're looking for one:
-The pistol grip for the shooting hand must not rest on the sling or on your other arm.
-No perforation of the barrel or extension tubes is allowed.
-There must be nothing special inside the barrel or extension tube other than rifling & chambering.
-No compensators or muzzle brakes allowed.
-You may use electronic triggers, if the entire assembly is firmly attached to and contained within the action or stock of the rifle, the trigger is operated by your right hand if you shoot right-handed (and vice versa), every part of it is present when the rifle is inspected, and if it doesn't cause the rifle to be oversized or overweight (duh).
-Slings: Maximum width 40mm (1.57"); may only be used on upper part of non-trigger arm and from there go to the forend, attached at a single point; may only pass along one side of the hand or wrist; may not touch the rifle except at the swivel and hand stop.
-Barrel weights may be used within a radius of 30mm (1.18") from the center of the bore, and may be moved along its length.
300m Standard Rifle Only:
-Butt plates may be adjustable up/down, left/right, but may not swivel.
-Prohibited stock features: thumb hole, thumb rest, palm rest, heel rest, spirit level, grip-increasing material.
-Minimum trigger pull: 1500g (3.3 lbs).
-Maximum barrel length: 762mm (30").
Obviously, there's much to consider, and sight info is on the next page. This only covers the basics... for complete rules, go straight to the source: USA Shooting (USAS).