I'm not sure the question is well posed. If you are interested in conductors stretching infinitely along one direction, e.g. an ideal transmission line, you should perform a 2D simulation (which is possible in FasterCap).
Instead if you are interested in a 3D object, then I do not see how this can be infinitely thick unless this also has an infinite surface e.g. a halfspace plane (or, actually I can see it, but I find no reason why you should be using this hypotesis  but I may fail to understand the underlying reason). In this case the answer is that you can not define them, as FastCap and FasterCap do not support infinite planes. Actually an infinite plane must be an approximation for a real, finite extent plane, and is used / defined in some solvers as it may be more efficient for dealing with some cases. You can anyway consider a finite dimension plane, as large as your real plane or, if that is not efficient, large enough to be 'infinite' with respect to the structure you are considering on top of the plane. Let's remember in this context that you cannot 'see' anything through a conductive plane  if you have an infinite ground plane, it does not matter at all if it is infinitely thick or not. A dielectric plane is a bit different. If not large enough, you should also 'close' the sides to be sure that the conditions at the interface are physically sound.
Best, Enrico
