To provide a thermoplastic elastomer composition which is used for blocks for guiding a visually handicapped person, gives a block with little residual dent and is excellent in scratching resistance, adherence to concrete, extrusion and injection molding, and the blocks made from the elastomer composition.

The thermoplastic elastomer composition used for blocks for guiding a visually handicapped person is characterized in that it is obtained by melting and kneading a composition containing (a) 100 pts.wt. of a block copolymer and/or a hydrogenated block copolymer, consisting of at least two polymer blocks A comprising mainly an aromatic vinyl compound and at least one polymer block B comprising mainly a conjugated diene compound, (b) 15-200 pts.wt. of an olefin resin decomposable by a peroxide, (c) 0.2-3.5 pts.wt. of an organic peroxide, and (d) 150-350 pts.wt. of an inorganic filler. A sheet, tile or block unit is provided which is obtained by fabricating the composition and used for blocks for guiding a visually handicapped person. A concrete block is provided, which is made from the composition and used for guiding a visually handicapped person.