Single-crystal elastic constants of A1 (fee disordered) and single-variant L10-ordered FePd alloy are presented. The ordered phase consisting of single-variant domains was formed using the compression method proposed by our previous paper [T. Ichitsubo, M. Nakamoto, K. Tanaka, and M. Koiwa, Mater. Trans. JIM 39, 24 (1998)]. A complete set of elastic constants has been determined with the resonance ultrasound spectroscopy technique. The disordered alloy exhibits common features of usual fee metals, and the ordered alloy clearly shows a tetragonal elastic anisotropy, c11<c33 and c44<c66. The temperature dependence of the moduli has also been investigated using a quenched disordered sample. The anisotropy factor 2c44/(c11-c12) is fairly large (about 3.0) at any temperatures, which may be related with the tweed pattern formation observed experimentally in the early stage of ordering.