We have measured the II-band light curve of the black hole binary V404
Cyg (=GS 2023+338). When folded at the spectroscopic orbital period,
6.4714 days, the light curve has two maxima and two minima per orbit a
nd a peak-to-peak amplitude of similar to 0.25 mag. This variation is
produced primarily by ellipsoidal variations of the KO IV star in the
system, but the light curve is distorted by other sources of variabili
ty as well. Because of the distortions and because of an unknown contr
ibution to the infrared flux from the accretion disk around the black
hole, analysis of the ellipsoidal variations yields only a lower limit
to the orbital inclination of V404 Cyg and, thus, an upper limit to t
he mass of its black hole. Our analysis of the H-band light curve yiel
ds an upper limit of 12.5 M(.). We show that previously published K-ba
nd light curves of V404 Cyg were probably also contaminated by other s
ources of variability. Reanalysis of the K-band data gives results con
sistent with the H-band data.