To the best of my knowledge the most commonly used Python Finite Element library is FiPy.
I use this library frequently, and i recommend it highly. It is a mature, stable project (current stable version is 2.1.2), currently maintained by its creator, the Materials Measurement Library of the US Government Institute, NIST.The documentation and (working) sample code are excellent. It's also relatively (for a specialized numerical library) simple to install; the only dependencies are NumPy, and PySparse (which are also dependencies for sfePy).
If you have tried to install this library in the past and had difficulty, you might want try again. The reason i say that is Trillinos (the distributed processing library for FiPy) is now a separate package (though i would still recommend using Trillinos if you want to parallelize FiPy computations)
(Note: you might also find useful, this Site: hpfem.org (a Site maintained by a consortium of three universities) maintains an excellent collection of FEM libraries and other resources.)
