The aim of this paper is to prove a type of uniqueness for the Dirichlet problem on a cylinder the special case of which is a strip in the plane. By defining generalized Poisson integrals with certain continuous functions on the boundary of a cylinder, we shall investigate the difference between them and harmonic functions having the same boundary value. Given any continuous function on the boundary of a cylinder, we shall also give a harmonic function with that function as the boundary value.
