Abstract: A resilient mat system has at least one mat with a mat thickness T, an upper layer with an upper layer thickness t, and a plurality of supporting resilient substructure columns, each column having a relatively uniform height h, such that T=t+h, wherein the ratio of h:t>3.5 for values of T> about 0.9 inch. Each column wall surrounds a central void in the column, the void opening at a bottom of the column. The column has in a bottom region of the column wall a lower zone that is a more compressible, relatively collapsible zone, and in an upper region of the column wall above the lower zone an upper zone that is a less compressible, relatively uncollapsible zone. The resilient mat system optionally has a relatively rigid ramp structure bordering at least one mat on at least two sides, and the ramp structure is preferably attached to a floor base to retain the mat, whereby the mat is removable from the border of the ramp. Alternatively, the ramp structure is attached to at least a portion of the mat.