  We use 3D computer modelling to investigate the timescales and radiative
output from maser flares generated by the impact of shock-waves on astronomical
unit-scale clouds in interstellar and star-forming regions, and in
circumstellar regions in some circumstances. Physical conditions are derived
from simple models of isothermal hydrodynamic (single-fluid) and C-type (ionic
and neutral fluid) shock-waves, and based on the ortho-H$_2$O 22-GHz
transition. Maser saturation is comprehensively included, and we find that the
most saturated maser inversions are found predominantly in the shocked
material. We study the effect on the intensity, flux density and duration of
flares of the following parameters: the pre-shock level of saturation, the
observer's viewpoint, and the shock speed. Our models are able to reproduce
observed flare rise times of a few times 10 days, specific intensities of up to
10$^5$ times the saturation intensity and flux densities of order
$100(R/d)^2$Jy from a source of radius $R$ astronomical units at a distance of
$d$ kiloparsec. We found that flares from C-type shocks are approximately 5
times more likely to be seen by a randomly placed observer than flares from
hydrodynamically shocked clouds of similar dimensions. We computed intrinsic
beaming patterns of the maser emission, finding substantial extension of the
pattern parallel to the shock front in the hydrodynamic models. Beaming solid
angles for hydrodynamic models can be as small as $1.3\times 10^{-5}$sr, but
are an order of magnitude larger for C-type models.
