The invention relates to a surface-area gantry system for machining, assembly and handling tasks, with three axes of motion in the directions X, Y and Z, where the Z axis is provided with machining or grasping mechanisms, notably for the high-speed machining of non-metallic materials. The aim of the invention is to create an especially light and stiff surface-area gantry system suitable for large machining areas and universal applications which consists of simple components and linear modules which are economical to produce even in small numbers and permits relatively high feed rates and accelerations. According to the invention the X, Y and Z axes have linear modules (2) which are driven by synchronous linear motors and consist of a hot-rolled shaped support section (12) having a rectangular or square cross-section and fitted with pair-wise, opposite secondary elements (10). The slides (3) or working slides (1) are made of cast metal in the form of integral components -hich are provided with a wrap-around element (4) for the X, Y and Z axis and contain the primary elements (5).