The invention relates to an apparatus for compacting a continuous
textile substrate (T) by means of an elastic belt. The apparatus (1) comprises: a heatable rotating cylinder (10); an endless elastic belt (20); - a
system of rollers (31, 32, 33, 34, 35) whereupon said belt (20) is wrapped in an elongation pretensioned state according to a predetermined pretensioning degree. The roller
system comprises: - a set of three rollers consisting of a motorized drive roller (31), a motorized
brake roller (32), and a first idle return roller (33), which is arranged between said motorized drive roller and said motorized
brake roller; and - at least a second idle return roller (34). The motorized drive roller (31) and the motorized
brake roller (32) are actuatable so as to cause said belt (20) to slide along said
closed path by imposing upon said belt - according to a predetermined phase shifting degree of the respective tangential velocities - an additional elongation tension state. The motorized drive roller (31) is a
metal roller, wherein the cylindrical side surface thereof, intended to come into contact with said belt (20), is smooth with a roughness chosen such as to generate, in contact with the elastic belt, a
friction coefficient (f) which meets the following equation: T2T1≤efα where α is the wrap angle of the belt around the drive roller (31), T1 is the belt tension downstream of the roller, and T2 is the belt tension upstream of the roller, wherein the ratio T2 / T1 is a function of the predetermined pretensioning degree and the predetermined additional elongation tension state of the belt.