Article of clothing for biomechanical assistance to the torso of the user having worn said article, the latter comprising or incorporating an elastic sheath for functional assistance to at least one longitudinal segment of interest of the user's trunk; this elastic sheath having, by textile construction, in combination, the following technical characteristics: a) on either side of the posterior longitudinal element, defined below, the elastic sheath has perimetric elasticity, around the longitudinal axis of the article of clothing, and along at least a part of its height; b) this elastic sheath comprises at least one central posterior longitudinal element, aligned with or on the spine of the user wearing the article of clothing; c) on either side of the central posterior longitudinal element, the elastic sheath comprises two returns (61, 62) of the user's trunk covered by the article of clothing; each said return extends at or along the surface of the sheath, from said central posterior longitudinal element, towards the anterior part of the sheath; and these two returns (61, 62) leaving at least one central and anterior portion of said sheath, free from any strapping, other than the elastic strapping inherent in the wearing of the article of clothing, and therefore of the functional assistance elastic sheath; and d) the perimeter elasticity of the elastic sheath determines an internal volume, in the initial, deployed state, i.e. when the article of clothing is not worn by the user, at most equal to 90% of the external volume of the longitudinal segment of interest of the user's trunk; e) each return (61 or 62) of the user's trunk comprises a textile section extending to a continuous edge (611 or 621) comprising one or more portions located outside or beyond the posterior side of the elastic sheath, in particular the side anterior to the latter, and having a transverse elasticity, less important than the perimetric or transverse elasticity of the elastic sheath, characterized in that: f) the central posterior longitudinal element is a transverse anchoring element for the elastic sheath, having a lower transverse elasticity than its longitudinal elasticity. a) on either side of the posterior longitudinal element, defined below, the elastic sheath has perimetric elasticity, around the longitudinal axis of the article of clothing, and along at least a part of its height; b) this elastic sheath comprises at least one central posterior longitudinal element, aligned with or on the spine of the user wearing the article of clothing; c) on either side of the central posterior longitudinal element, the elastic sheath comprises two returns (61, 62) of the user's trunk covered by the article of clothing; each said return extends at or along the surface of the sheath, from said central posterior longitudinal element, towards the anterior part of the sheath; and these two returns (61, 62) leaving at least one central and anterior portion of said sheath, free from any strapping, other than the elastic strapping inherent in the wearing of the article of clothing, and therefore of the functional assistance elastic sheath; and d) the perimeter elasticity of the elastic sheath determines an internal volume, in the initial, deployed state, i.e. when the article of clothing is not worn by the user, at most equal to 90% of the external volume of the longitudinal segment of interest of the user's trunk; e) each return (61 or 62) of the user's trunk comprises a textile section extending to a continuous edge (611 or 621) comprising one or more portions located outside or beyond the posterior side of the elastic sheath, in particular the side anterior to the latter, and having a transverse elasticity, less important than the perimetric or transverse elasticity of the elastic sheath,