OK, as above it may be the graphics card, or the cable even. [Seeing that it has happened to 2 monitors]. But I have seen the same, or very similar problem before, and it was the monitor causing the problem, even a replacement of the same make had the same problem, and it was only the second re-placement, [Under warranty] that cured it.
Try the following. Place one hand either side of the monitor, so that you thumb is on the front bezel, and your fingers on the sides of the case, squeeze your fingers and see if the lines disappear! If they do, but come back again when you remove your hands from monitor, then that is the problem and will require replacing.
If the above doesn't make any difference, then you will need to check that the graphics card is working correctly. This card is inside the PC, and if you are not sure where to look or how to remove/replace, then post back on this same thread, and I or one of the other forum users will try to help. j.