  Recently it has been found that models of massive stars reach the Eddington
limit in their interior, which leads to dilute extended envelopes. We perform a
comparative study of the envelope properties of massive stars at different
metallicities, with the aim to establish the impact of the stellar metallicity
on the effect of envelope inflation. We analyse published grids of
core-hydrogen burning massive star models computed with metallicities
appropriate for massive stars in the Milky Way, the LMC and the SMC, the very
metal poor dwarf galaxy I Zwicky 18, and for metal-free chemical composition.
Stellar models of all the investigated metallicities reach and exceed the
Eddington limit in their interior, aided by the opacity peaks of iron, helium
and hydrogen, and consequently develop inflated envelopes. Envelope inflation
leads to a redward bending of the zero-age main sequence and a broadening of
the main sequence band in the upper part of the Hertzsprung-Russell diagram. We
derive the limiting L/M-values as function of the stellar surface temperature
above which inflation occurs, and find them to be larger for lower metallicity.
While Galactic models show inflation above ~29 Msun, the corresponding mass
limit for Population III stars is ~150 Msun. While the masses of the inflated
envelopes are generally small, we find that they can reach 1-100 Msun in models
with effective temperatures below ~8000 K, with higher masses reached by models
of lower metallicity. Envelope inflation is expected to occur in sufficiently
massive stars at all metallicities, and is expected to lead to rapidly growing
pulsations, high macroturbulent velocities, and might well be related to the
unexplained variability observed in Luminous Blue Variables like S Doradus and
Eta Carina.
