1968 Cent- What Would Cause It To Concave?

Could it be because the coin has a high relief ?

That's just the way they were that year. The following year they redid the master hub, the bust is a little smaller, the relief is still high dut the bust is more detailed. If you put a 69 next to a 68 you can see they made a lot of changes. The major reason for the changes was because over the years the master hub had spread and lost detail. Notice how the lettering is alll the way out to the rims and is merging up into it. On the 69's the lettering is sharper and has been moved away from the rim. You can see the same type of thing on the 1981 to 83 nickels. The 81's are from older worn master hubs with the lettering out close to the rims. on the 83's the lettering is sharper and has been moved away from the rims. The 1982's can be found with both types of hubs and can be found in four different varieties from each mint. Most people don't even know about these varieties.

Don't look at the 1973's. The rim is even higher than that 68 your looking at.