Method for producing a fibrous mat which is without resins and/or amalgams and is designed to be installed in a silencer of an exhaust gas system of an internal combustion engine of a vehicle to attenuate the noise and heat associated with the gas passing through it; said fibrous mat is designed to be wrapped around, or fitted/inserted in associated pipes, tubular perforated partitions, exhaust ducts/channels passing through a chamber of said silencer, said method comprises the steps of: a) providing a fibrous core comprising at least one fibrous bundle that at least partially extends along a direction approximately parallel to a longitudinal axis, b) wrapping said fibrous core by means of at least one fibrous bundle in order to form one or more coils that extend transverse to said bundle of said fibrous core for internally retaining said fibrous bundle of said fibrous core, said method being characterised by the fact that: said step a) comprises the step of winding said fibrous bundle around two axes and that are perpendicular to said longitudinal axis and are mutually spaced at a distance approximately equal to the length of said fibrous mat so as to form an elongated wound skein that extends along said longitudinal axis, said step b) comprises the step of wrapping the outer surface of said fibrous core by means of said fibrous bundle so as to provide at least one outer tubular fibrous containment sleeve that extends, in turn, along said longitudinal axis and at least partially covers said outer surface of the fibrous core so as to trap it therein, and wherein said fibrous core and said outer tubular fibrous containment sleeve comprises mineral fibres which attenuate the noise/heat transmission due to the exhaust gas passing through the ducts, and the inner space of said outer tubular fibrous containment sleeve is filled by said fibrous core, said fibrous core being simultaneously trapped by said outer tubular fibrous containment sleeve. a) providing a fibrous core comprising at least one fibrous bundle that at least partially extends along a direction approximately parallel to a longitudinal axis, b) wrapping said fibrous core by means of at least one fibrous bundle in order to form one or more coils that extend transverse to said bundle of said fibrous core for internally retaining said fibrous bundle of said fibrous core, said step a) comprises the step of winding said fibrous bundle around two axes and that are perpendicular to said longitudinal axis and are mutually spaced at a distance approximately equal to the length of said fibrous mat so as to form an elongated wound skein that extends along said longitudinal axis, said step b) comprises the step of wrapping the outer surface of said fibrous core by means of said fibrous bundle so as to provide at least one outer tubular fibrous containment sleeve that extends, in turn, along said longitudinal axis and at least partially covers said outer surface of the fibrous core so as to trap it therein, and wherein said fibrous core and said outer tubular fibrous containment sleeve comprises mineral fibres which attenuate the noise/heat transmission due to the exhaust gas passing through the ducts, and the inner space of said outer tubular fibrous containment sleeve is filled by said fibrous core, said fibrous core being simultaneously trapped by said outer tubular fibrous containment sleeve.