  We present a method for the calculation of the effects of external
irradiation on the geometrical shape of the secondary in a close binary
containing a compact star, the source of the radiation, and a normal companion
star, where we include the possibility of shadowing by an accretion disc. The
model is based on a simple modification of the standard Roche binary potential
in which the radiation-pressure force is parameterised using the ratio of the
radiation to the gravitational force. We have constructed numerical solutions
of approximate 3-dimensional irradiated equipotential surfaces to demonstrate
the main geometrical effects of external radiation pressure. For systems in
which the inner Lagrangian point is irradiated directly and for sufficiently
high irradiation fluxes, the critical condition for which the secondary fills
its tidal lobe changes from an inner to an outer critical configuration, where
the critical equipotential surface connects to one of the outer rather than the
inner Lagrangian point. Such a situation may apply to evaporating binary pulsar
systems (e.g. PSR 1957+20), stars orbiting supermassive black holes in AGN and
some high-mass X-ray binaries (including Centaurus X-3). For systems containing
an accretion disc, which shadows the inner Lagrangian point from the external
irradiation, the presence of significant radiation pressure causes a
non-axisymmetric deformation of the stellar surface. We have calculated
modified Roche potentials to determine the main effects on the optical
lightcurves and radial velocity curves for typical binary parameters. Compared
to previous studies, the inclusion of irradiation-pressure effects results in
changes in the derived system parameters (e.g. component masses, radial
velocities) that may be as high as 30 per cent.
