Combine shortening and sugar; beat well. Add eggs, one at a time, beating well after each addition. Stir in vanilla. Combine flour, baking powder, and salt; add to creamed mixture, mixing well. Fold in apricots and pecans.
Press mixture evenly into a greased 13- x 9- x 2-inch baking pan. Bake at 350° for 18 to 20 minutes. Cool completely, and cut into 2- x 1-inch bars.