A modular mat comprises mirror image layers. At least one fitting receiver is integrally formed in a central portion of each layer, and at least one aperture is formed in a flange portion of each layer. The layers are congruently mated and affixed such that the fitting receiver of one layer is disposed through a corresponding aperture of the flange of the opposite layer. The outer surfaces of the layers comprise traction elements, which may be of different grades, such as industrial grade on one layer and pedestrian grade on the opposing layer. A floor covering system is also disclosed comprising a plurality of modular mats disposed in partially overlapping and interlocking relation with adjacent mats.