Descendants of LDS Church founder Joseph Smith and his brother, Hyrum, have established a family foundation to help beautify, landscape and enhance grave sites of their forebears at the Smith Homestead in Nauvoo, Ill.

Construction on the site began Wednesday and is scheduled to be completed by August. More than 20 graves, including those of Joseph and Hyrum Smith; their brothers, Samuel and Don Carlos; their parents, Joseph Smith Sr. and Lucy Mack Smith; Joseph's wife, Emma; and three of Joseph and Emma's children - Frederick G. W., Don Carlos, and an unnamed child - are part of the family plot.A pamphlet explaining the purpose of the foundation says the effort represents "an opportunity for descendants of Joseph and Hyrum to work together on a project for possibly the first time in 150 years. This will certainly have far-reaching benefits."

Eldred G. Smith, a direct descendant of Hyrum Smith and patriarch emeritus of The Church of Jesus Christ of Latter-day Saints, serves as co-chairman of the foundation, along with Wallace B. Smith, president of The Reorganized Church of Jesus Christ of Latter-day Saints and a direct descendant of Joseph Smith. The Reorganized Church, headquartered in Independence, Mo., owns the property where the cemetery rests.

Officers and trustees of The Joseph and Hyrum Smith Family Foundation hope to raise $120,000 to fund and maintain the project. Funds will be used to enlarge and open the area to the public, add new walks, benches and lighting, identify grave sites, lay new markers and plant trees and flowers.

The foundation is urging every family member, including small children, to contribute and attend the dedication ceremonies. Contributions from the public will also be accepted. Checks should be made payable to The Joseph and Hyrum Smith Family Foundation. Mailing address is: Elder M. Russell Ballard, Council of the Twelve, 47 E. South Temple, Salt Lake City, 84150.

A formal dedication ceremony is planned for Aug. 3, 1991, in Nauvoo. At that time, family members plan to bury a time capsule including names of all family members, noting those who contributed, and family memorabilia.

Emma Smith expressed her concern about the family cemetery in a letter to her son, Joseph Smith III, in 1867:

"I have always felt sad about the neglected condition of that place, and as I do not expect ever to be able to build me a house to live in, I would like to fix a place to be put away when I have done all my work on the earth.

"Joseph, I would like if you are able to extend that fence so as to enclose the graves of your two little brothers. I have got twenty-five dollars that no one has any right to but myself . . . I feel anxious to apply that money on the graveyard.

"After I have done that, I think we can ask our Smith relations to help mark Father's and Mother's graves, if no more."

Family representatives have contacted many family members, and are interested in identifying those who are not on family lists. Those wanting more information or wishing to be added to the list may write to Eldred G. Smith, 2942 Devonshire Circle, Salt Lake City, 84108, or call 582-9610.