An apparatus for applying an elastic tubular sleeve onto a splicing region between at least one pair of cables, wherein the tubular sleeve is supported in a radially expanded condition on at least one supporting element, may include axial-movement devices configured to axially move the at least one supporting element relative to the tubular sleeve at an adjustable speed, so as to cause a radial elastic shrinkage of the tubular sleeve capable of inducing an axial ejection thrust on the at least one supporting element, and counter devices configured to counteract the axial ejection thrust induced by the elastic shrinkage of the tubular sleeve.