  The helioglow is a fluorescence of interstellar atoms inside the heliosphere,
where they are excited by the solar EUV emission. So far, the helioglow of
interstellar H and He have been detected. The helioglow features a
characteristic distribution in the sky, which can be used to derive both the
properties of interstellar neutral gas and those of the solar wind. This
requires a simulation model capable of catching with a sufficient realism the
essential coupling relations between the solar factors and interstellar. The
solar factors include the solar wind flux and its variation with time and
heliolatitude, as well as the heliolatitude and time variation of the solar EUV
output. The ISN gas inside the heliosphere features a complex distribution
function, which varies with time and location. The paper presents the first
version of a WawHelioGlow simulation model for the helioglow flux using an
optically thin, single scattering approximation. The helioglow computations are
based on a sophisticated kinetic treatment of the distribution functions of
interstellar H and He provided by the (n)WTPM model. The model takes into
account heliolatitudinal and spectral variations of the solar EUV output from
observations. We present a formulation of the model and the treatment of the
solar spectral flux. The accompanying Paper II illustrates details of the line
of sight evolution of the elements of the model and a brief comparison of
results of the WawHelioGlow code with selected sky maps of the hydrogen
helioglow, obtained by the SWAN instrument onboard the SOHO mission.
