This paper deals with the set inversion problem X = f −1 (Y) in the case where the function f : R n → R m and the set Y are both uncertain. The uncertainty is treated under the form of intervals. More precisely, for all x, f (x) is inside the box [f ](x) and the uncertain set Y is bracketed between an inner set Y ⊂ and an outer set Y ⊃. The introduction of new tools such as thick intervals and thick boxes will allow us to propose an efficient algorithm that handles the uncertainty of sets in an elegant and efficient manner. Some elementary test-cases that cannot be handled easily and properly by existing methods show the efficiency of the approach.