Using the Monte Carlo method, we determine the free energy of the inte
rface of the 3D Ising model in the scaling region. By integrating the
interface energies over the inverse temperature beta, we obtain estima
tes for the free energies of interfaces with cross sections up to 96 x
96, and for a range 0.223 less than or equal to beta less than or equ
al to 0.23. Our data yield a precise estimation of the interface tensi
ons a. We determine the amplitude sigma(0) in the critical law sigma s
imilar to sigma(0)t(mu) and estimate the combination sigma xi(2) which
yields the universal constant R_ in the critical limit.