Although multi-element antenna (MEA) systems are already used in some modern wireless communication systems, the issue of mutual coupling between elements remains a challenge during MEA system design. Indeed, communications engineers continue to bemoan the fact that that the antenna elements are often still designed with such coupling as an afterthought. Thus, some authors have used the decoupling surface (DS) idea, whereby a separate DS is added to the MEA systems to reduce the above coupling. Whereas a DS may indeed lower the coupling levels between the elements of a given MEA system, it usually changes the other performance parameters as well, and in an undesirable way. Thus, this design route is a complicated one that is not easily affected. In this thesis we propose, for the first time, a new design process for MEA systems based on shape synthesis. The MEA system performance indicators are combined into an objective that sets the goal of the shape synthesis procedure. The application of the proposed design process is illustrated for three different geometrical arrangements of patch antennas and decoupling surfaces. This confirms the efficacy of the new design method.