ANSYS, ABAQUS(now SIMULIA, the Dassault Systèmes brand for Realistic Simulation), and NASTRAN are the three popular FEA codes.
Most FEA applications in industry is done under some QA/QC system so open source is not used. The code and its application have to be approved in the nuclear and aerospace industries.
http://www.ansys.com/
http://www.simulia.com/
NASTRAN is perculiar because there are now several developers.
http://en.wikipedia.org/wiki/Nastran#NASTRAN_Options
COMSOL is a newbie to the field.
http://www.comsol.com/
All of them seem to have some academic licensing arrangement. Check with one's university or MechEng/AeroEng departments.