This paper deals with geometric shape optimization of a parallelepipedic fixed-bed reactor with single phase liquid flow where a chemical reaction takes place. The packing is a sort of static mixer made up of solid cylindrical obstacles uniformly distributed in the reactor. The reactive flow is described by means of momentum and mass transport equations in laminar flow regime. The objective is to determine the shape of the packing which maximizes the reaction conversion rate subjected to some specified manufacturing constraints. The optimization approach developed is based on the adjoint system method and the results show that the opti- mal shape obtained allows to significantly improve the reaction conversion rate. Furthermore, the optimal shape is printed by means of an additive manufacturing technique and several manufacturing constraints mainly related to the thickness of packing are considered.