We do not have a perfect grass for heavily shaded areas and sometimes have to go to groundcovers to cover these areas. If the area is lightly shaded, you will have some success with St. Augustine grass but it still needs at least four hours to survive and six hours to really flourish. Bermudagrasses need full sun and will not tolerate shade. Buffalograss must have full sun. Zoysia needs six to eight hours of sun to flourish. Tall Fescue has good shade tolerance but is a cool season grass and has little tolerance of our hot, dry summers.
I think St. Augustinegrass is still the best for lightly shaded areas and sometimes you can trim up limbs on trees or shrubs to allow more sun to get to the grass. Be careful when you do this and be sure you are not destroying the look of the landscape by poor choices in trimming. You may decide that groundcovers or hardscapes are the answer to your shaded areas. They can be quite beautiful and add interest to your landscape.
You will find more information about lawn grasses and ornamental grasses in the real dirt A Gardening Handbook for Parker County.