Steady-state waves impinging obliquely on a coast are used to model a
tsunami wave train as it moves from the open sea onto a continental sh
elf The shelf edge is modelled with a discontinuity in depth, and on t
he landward side of the shelf edge the mean depth decreases linearly w
ith distance to a value of zero at the coast line. Reflected waves in
the open sea are found to have a reflection coefficient of unity as a
result of a requirement that the solution be bounded at the shore line
. The angle of wave incidence is found to have a significant effect up
on wave amplifications near resonance frequencies but to have very lit
tle effect upon the magnitude of these resonance frequencies. Wave per
iods and wave length components parallel to the shore line are not cha
nged as waves pass over the shelf, but wave length components normal t
o the shore line change significantly in this region.