In this article we prove for 1 < p < ∞ the existence of the L p -Helmholtz projection in finite cylinders Ω. More precisely, Ω is considered to be given as the Cartesian product of a cube and a bounded domain V having C 1-boundary. Adapting an approach of Farwig (2003), operator-valued Fourier series are used to solve a related partial periodic weak Neumann problem. By reflection techniques the weak Neumann problem in Ω is solved, which implies existence and a representation of the L p -Helmholtz projection as a Fourier multiplier operator.