Summary: In this paper we establish the existence of periodic travelling waves for a 2D Boussinesq type system in three-dimensional water-wave dynamics in the weakly nonlinear long-wave regime. For wave speed \(|c|>1\) and large surface tension, we are able to characterize these solutions through spatial dynamics by reducing a linearly ill-posedmixed type initial value problem to a center manifold of finite dimension and infinite codimension. We will see that this center manifold contains all globally defined small-amplitude solutions of the travelling wave equation for the Boussinesq system that are periodic in the direction of propagation.