A tread for a tire having a contact face intended to come into contact with ground during rolling, the tread being provided with at least one principal groove of a depth Dp, and a plurality of sub grooves of a depth Ds extending in an orientation with an angle relative to an orientation the at least one principal groove being extending, the at least one principal groove and the plurality of sub grooves delimiting a plurality of contact elements, a material constituting the plurality of contact elements having a modulus G* at 60°C Mb and a glass transition temperature Tgb, at least one of a contact element among the plurality of contact elements being provided with a covering layer covering at least one of a lateral face of the contact element facing to circumferential orientation at least partly, the covering layer consisting of at least two layers, an outer covering layer facing to outward of the contact element, a material constituting the outer covering layer has a modulus G* at 60°C Mo and a glass transition temperature Tgo, and an inner covering layer facing to inward of the contact element, a material constituting the inner covering layer has a modulus G* at 60°C Mi and a glass transition temperature Tgi, the tread being characterized in that the modulus G* at 60°C Mb of the material constituting the contact element is higher than the modulus G* at 60°C Mi of the material constituting the inner covering layer, and wherein the modulus G* at 60°C Mo of the material constituting the outer covering layer is higher than the modulus G* at 60°C Mb of the material constituting the contact element and/or the glass transition temperature Tgb of the material constituting the contact element is higher than the glass transition temperature Tgi of the material constituting the inner covering layer, and wherein the glass transition temperature Tgo of the material constituting the outer covering layer is higher than the glass transition temperature Tgb of the material constituting the contact element, the modulus G* Mb, Mo and Mi being measured according to ASTM D 5992-96 standard by subjecting the material to a simple alternating sinusoidal shear load at a frequency of 10 Hz under a maximum shear stress imposed of 0.7 MPa. at least one of a contact element among the plurality of contact elements being provided with a covering layer covering at least one of a lateral face of the contact element facing to circumferential orientation at least partly, the covering layer consisting of at least two layers, an outer covering layer facing to outward of the contact element, a material constituting the outer covering layer has a modulus G* at 60°C Mo and a glass transition temperature Tgo, and an inner covering layer facing to inward of the contact element, a material constituting the inner covering layer has a modulus G* at 60°C Mi and a glass transition temperature Tgi, the tread being characterized in that the modulus G* at 60°C Mb of the material constituting the contact element is higher than the modulus G* at 60°C Mi of the material constituting the inner covering layer, and wherein the modulus G* at 60°C Mo of the material constituting the outer covering layer is higher than the modulus G* at 60°C Mb of the material constituting the contact element and/or the glass transition temperature Tgb of the material constituting the contact element is higher than the glass transition temperature Tgi of the material constituting the inner covering layer, and wherein the glass transition temperature Tgo of the material constituting the outer covering layer is higher than the glass transition temperature Tgb of the material constituting the contact element, the modulus G* Mb, Mo and Mi being measured according to ASTM D 5992-96 standard by subjecting the material to a simple alternating sinusoidal shear load at a frequency of 10 Hz under a maximum shear stress imposed of 0.7 MPa.