Theoretical and computational results are presented for the interactio
n forces among multiple ships or bodies which are operating near to ea
ch other. These computations are made under several assumptions, the m
ost important of which is that the free surface is rigid. An assumptio
n usually made in the analysis of this problem is that the ships are s
lender, but the approach taken here is fully three-dimensional. The me
thod is applicable to any number of arbitrarily shaped bodies in arbit
rary motion in a fluid domain which may be bounded by irregular surfac
es. Results are presented for the simple case of two ships passing in
a canal of rectangular cross section, for which a particular Green fun
ction greatly reduces the computational effort; and for two ships pass
ing in a canal with sloping sides, for which no such economies are ava
ilable.