A non-elastic foam-fabric composite band (14; 40; 60) for use in orthopedic braces and supports comprising:- a) a first layer of an elastic bi-laminate (16, 18, 20; 42, 44, 46; 62) comprising an elastic foam layer (18; 44; 64) and an elastic fabric layer (20; 46; 66), the elastic foam layer (18; 44; 64) extending the length and width of the elastic fabric layer (20; 46; 66) and being laminated thereto, the elastic foam layer (18; 44; 64) having an open-cell frictional gripping surface (18A; 42A; 62A) and positive moisture wicking characteristic; b) a second layer of unbroken loop material (22; 48; 68) extending the length of the elastic bi-laminate (16, 18, 20; 42, 44, 46; 66), the second layer of unbroken loop material (22; 48; 68) comprising a lengthwise non-elastic strip having an outer layer (22A; 48A; 68A) of loops on a non-elastic backing layer (22B; 48B; 68B), and being secured to the elastic fabric layer (20; 46; 66) of the elastic bi-laminate (16, 18, 20; 42, 44, 46; 66) opposite the elastic foam layer (18; 44; 64), along the length thereof, the elastic foam layer (18; 44; 64) and elastic fabric layer (20; 46; 66) being rendered lengthwise non-stretchable along their entire secured lengths by the second layer of unbroken loop material (22; 48; 68) secured thereto; and c) a hook and loop fastener construction comprising a loop element formed by the second layer of unbroken loop material (22; 48; 68) and a hook tab (24; 52; 72) secured proximate one end of the second layer of unbroken loop material (22; 48; 68), the hook and loop fastener construction being configured for securing the hook tab (24; 52; 72) to the outer layer (22A; 48A; 68A) of loops. a) a first layer of an elastic bi-laminate (16, 18, 20; 42, 44, 46; 62) comprising an elastic foam layer (18; 44; 64) and an elastic fabric layer (20; 46; 66), the elastic foam layer (18; 44; 64) extending the length and width of the elastic fabric layer (20; 46; 66) and being laminated thereto, the elastic foam layer (18; 44; 64) having an open-cell frictional gripping surface (18A; 42A; 62A) and positive moisture wicking characteristic; b) a second layer of unbroken loop material (22; 48; 68) extending the length of the elastic bi-laminate (16, 18, 20; 42, 44, 46; 66), the second layer of unbroken loop material (22; 48; 68) comprising a lengthwise non-elastic strip having an outer layer (22A; 48A; 68A) of loops on a non-elastic backing layer (22B; 48B; 68B), and being secured to the elastic fabric layer (20; 46; 66) of the elastic bi-laminate (16, 18, 20; 42, 44, 46; 66) opposite the elastic foam layer (18; 44; 64), along the length thereof, the elastic foam layer (18; 44; 64) and elastic fabric layer (20; 46; 66) being rendered lengthwise non-stretchable along their entire secured lengths by the second layer of unbroken loop material (22; 48; 68) secured thereto; and c) a hook and loop fastener construction comprising a loop element formed by the second layer of unbroken loop material (22; 48; 68) and a hook tab (24; 52; 72) secured proximate one end of the second layer of unbroken loop material (22; 48; 68), the hook and loop fastener construction being configured for securing the hook tab (24; 52; 72) to the outer layer (22A; 48A; 68A) of loops.