A tubular covering sleeve for electric-cable joints is disposed on a supporting element causing radial expansion of said sleeve (2) starting from axially opposite end portions (7a) of the sleeve (2) itself. The tubular sleeve (2) in a radially expanded condition is installed on the supporting element (3). A apparatus (1) for putting into practice the above described method comprises a support (4) for the tubular sleeve (2) and a pair of expanders (10) to be located to a position substantially coaxial with said sleeve (2), each at a respective end (7) of the sleeve (2) itself. Driving means (11) is used for introducing the expanders (10) into the respective sleeve ends (7) and causing radial expansion. The apparatus (1) further comprises devices adapted to dispose the sleeve (2) in a radially expanded condition on the supporting element (3).