Cream butter in a large mixing bowl; add sugar, beating well. Add eggs; beat well.
Sift together flour, salt, and soda in a medium mixing bowl; add to creamed mixture, stirring well. Add vanilla and pecans, stirring well.
Divide dough in half; shape each half into a roll, 1 1/2 inches in diameter. Wrap each roll in waxed paper; chill until firm.
Remove waxed paper, and cut rolls into 1/4-inch-thick slices. Place 2 inches apart on lightly greased cookie sheets. Bake at 375° for 6 to 8 minutes or until lightly browned. Remove from cookie sheets, and cool on wire racks. Store in airtight containers.