The ability to form closed cavities inside the part printed is an important feature of Fused Filament Fabrication technology. A typical part consists of a dense shell bearing the primary load, filled with low-density plastic scaffold (infill). Such a constitution of the part provides in most cases appropriate strength and low weight. However, if the printed part shape includes horizontal (orthogonal to printer's Z axis) flat surfaces other than its top and bottom surface, then the shell of the part becomes interrupted, which may lead to drastic drop in the ability of the part to withstand loads. In the current study, a representative sample of a part with interrupted shell and testing apparatus is developed. Influence of shell and base thicknesses, as well as influence of the infill density on the part strength, are studied. Different approaches to the sample shape modification were applied and tested. The part shape optimization made with respect to peculiarities of Fused Filament Fabrication technology resulted in increment of the force, required to fracture the part from 483 to 1096 N and in decreased part mass from 36.9 to 30.2 g.