We discuss existence, uniqueness, and regularity of the solutions of a boundary value problem in a strip, which is obtained by linearization of the equations of the wave-resistance problem for a cylinder semisubmerged in a heavy fluid of constant depth
H
H
and moving at uniform velocity
c
c
in the direction orthogonal to its generators. We show that the problem has a unique solution, rapidly decreasing at infinity, for every
c
>
g
H
c > \sqrt {gH}
, where
g
g
is the acceleration of gravity. For
c
>
g
H
c > \sqrt {gH}
, we prove unique solvability provided
c
≠
c
k
c \ne {c_k}
, where
c
k
{c_k}
is a known sequence monotonically decreasing to zero. In this case, the related flow has in general nontrivial oscillations at infinity downstream.