  The atmospheric Cerenkov imaging technique has been used to search for
point-like and diffuse TeV gamma-ray emission from the southern supernova
remnant, W28, and surrounding region. The search, made with the CANGAROO 3.8m
telescope, encompasses a number of interesting features, the supernova remnant
itself, the EGRET source 3EG J1800-2338, the pulsar PSR J1801-23, strong 1720
MHz OH masers and molecular clouds on the north and east boundaries of the
remnant. An analysis tailored to extended and off-axis point sources was used,
and no evidence for TeV gamma-ray emission from any of the features described
above was found in data taken over the 1994 and 1995 seasons. Our upper limit
(E>1.5 TeV) for a diffuse source of radius 0.25deg encompassing both molecular
clouds was calculated at 6.64e-12 photons cm^-2 s^-1 (from 1994 data), and
interpreted within the framework of a model predicting TeV gamma-rays from
shocked-accelerated hadrons. Our upper limit suggests the need for some cutoff
in the parent spectrum of accelerated hadrons and/or slightly steeper parent
spectra than that used here (-2.1). As to the nature of 3EG J1800-2338, it
possibly does not result entirely from pi-zero decay, a conclusion also
consistent with its location in relation to W28.
