A modular oscillating head, particularly for stretching and softening industrial hides and similar products, comprising flexible mats (31, 32) for the continuous longitudinal advancement of the hides between at least one pair of plates with facing tools upon which actuation means act for producing their relative oscillation along a working plane (n) substantially perpendicular to that of the advancement. Two moving plates (7, 8) are provided anchored to respective beating bodies (3, 4) positioned on opposite sides with respect to a fixed supporting structure (2) along the working plane (π). The beating bodies (3, 4) are provided with a symmetrical oscillating movement with respect to the central structure in the working plane (π). The actuation means comprise a pair of connecting rod and crank mechanisms acting on the transverse end portions of the beating bodies, and are formed by connecting rods (11, 12; 21, 22) connected to respective eccentric cams (15, 16; 25, 26) having an angular staggering (B) substantially equal to 180° for producing the alternated symmetrical motion in opposite phase of the beating bodies (3, 4).