memory material 90 and the others are made from agglomerate elastic foam materials having different density degrees in such a way as to maintain an individual proprioception of instability in dynamic orthostatic but also static i e when still in place the mat with perimetric tray structure 10 is composed of at least a first layer of viscoelastic or memory material 90 with a density preferably d 50 kg m3 of about 2 3 cm in thickness beneath which is glued an elastic layer of a polyurethane foam with open cells 80 having a density preferably d 75 kg m3 of approximately 2 3 cm in thickness beneath which is glued in turn a base of cross linked closed cell polyethylene eva added 75 with a density preferably d 50 kg m3 which supports an external frame of closed cell polyethylene type ld29 70 of a density preferably d 180 kg m3 of about 5 cm in width and about 3 5 cm of thickness these layers constituting said mat with perimetric tray structure 10 for gymnastics and physical rehabilitation and re educational of open cell polyurethane foam 80 having a density preferably d 75 kg m3 about 2 3 cm thick and cross linked closed cell polyethylene eva added 75 with a density preferably d 50 kg m3 can also be constructed via an individual lamellar stratification of the said materials superimposed and joined in sandwich obtained by gluing of multi thin layers for obtaining the said desired individual thicknesses in order to avoid a deformation over time of the said materials caused by the load of the gymnastic work carried out on the same.