We present here a method used to solve the transfer equation in the in
terplanetary medium at Lyman alpha for realistic distributions of atom
ic hydrogen. To compute the source function in the heliosphere, we hav
e combined an iterative numerical solution for small values of optical
depth from the sun with a Monte Carlo simulation of radiative transfe
r at large optical depth. The intensity can then be computed by integr
ation of the source function along the line of sight, taking into acco
unt extinction. It is shown that radiative transfer effects on the sou
rce function are quite large, with a maximum increase in the downwind
region, depending on the interstellar and solar parameters. The discre
pancy between backscattered intensities computed using radiative trans
fer or optically thin approximation can also reach 40 % in the downwin
d cavity, even at a few AU from the sun. As a consequence, the solar a
nd interstellar parameters inferred from the study of Lyman alpha glow
must be reconsidered to take this effect into account. The upwind to
downwind intensity ratio computed at 1 AU from the sun is strongly mod
ified as well as the radial dependence of radial antisolar intensities
. The line width of the backscattered Lyman alpha profile is increased
by multiple scattering (14 % for n(infinity)=0.1 cm-3), thus modifyin
g the temperature inferred from optically thin approximation by 30 % a
t 0.1 cm-3. Finally, it is shown that methods to estimate the lifetime
at 1 AU of a hydrogen atom, by studying the maximum emissivity region
(MER), are little affected by radiative transfer calculations.