Sealed, thermally insulated tank has tank walls fixed to the load-bearing structure (1) of a floating structure, the tank walls having, in succession, in the direction of the thickness from the inside to the outside of the tank, a primary sealing barrier (8), a primary insulating barrier (6), a secondary sealing barrier (5) and a secondary insulating barrier (2), at least one of the insulating barriers includes juxtaposed non-conducting elements, each non-conducting element including a thermal insulation liner (63) and load-bearing elements that rise through the thickness of the thermal insulation liner in order to take up the compression forces, characterized in that the load-bearing elements of a non-conducting element include pillars (65) of small transverse section as compared to the dimensions of the non-conducting element in a plane parallel to the tank wall.