  In gamma-ray binaries such as LS 5039 a large number of electron-positron
pairs are created by the annihilation of primary very high energy (VHE)
gamma-rays with photons from the massive star. The radiation from these
particles contributes to the total high energy gamma-ray flux and can initiate
a cascade, decreasing the effective gamma-ray opacity in the system. The aim of
this paper is to model the cascade emission and investigate if it can account
for the VHE gamma-ray flux detected by HESS from LS 5039 at superior
conjunction, where the primary gamma-rays are expected to be fully absorbed. A
one-dimensional cascade develops along the line-of-sight if the deflections of
pairs induced by the surrounding magnetic field can be neglected. A
semi-analytical approach can then be adopted, including the effects of the
anisotropic seed radiation field from the companion star. Cascade equations are
numerically solved, yielding the density of pairs and photons. In LS 5039, the
cascade contribution to the total flux is large and anti-correlated with the
orbital modulation of the primary VHE gamma-rays. The cascade emission
dominates close to superior conjunction but is too strong to be compatible with
HESS measurements. Positron annihilation does not produce detectable 511 keV
emission. This study provides an upper limit to cascade emission in gamma-ray
binaries at orbital phases where absorption is strong. The pairs are likely to
be deflected or isotropized by the ambient magnetic field, which will reduce
the resulting emission seen by the observer. Cascade emission remains a viable
explanation for the detected gamma-rays at superior conjunction in LS 5039.
