The elastic constant, C', of Ce3S4 has been measured as a function of tempe
rature. It is shown that the curve is markedly different from that of La3S4
. Since the only ba sic difference between the two compounds is the existen
ce of a f-electron in Ce, we propose a theoretical scheme in which the f-el
ectron plays a crucial role. It is shown that the existence of the f-electr
on in Ce3S4 prevents the band Jahn-Teller type structural transition when t
he temperature is lowered. The theory is consistent with the experiment and
also with the theoretically predicted instability of cubic f-electron elem
ents at zero temperature.