A shock-absorbing support for damping vibrations between a rotor of a helicopter and its frame, wherein the rotor comprises a rotor mast connected to an engine via a transmission, said support comprising: - an outer annular body defining a central axis and adapted to be secured to the frame; - an inner bush coaxial with said outer annular body and adapted to be secured to the transmission of the rotor; - a substantially toroidal elastic member interposed between said outer annular body and said inner bush, said elastic member being made of an elastomeric material having a predetermined elastic constant; wherein said elastic member has two pairs of through slots (19, 19'; 20, 20') substantially parallel to said central axis, the slots (19, 19'; 20, 20') of each pair being diametrically opposite and symmetrical with respect to two first diametrical planes (π, π') intersecting at said central axis; wherein said first diametrical planes (π, π') are orthogonal to each other, said slots (19, 19'; 20, 20') having identical cross sections said slots (19, 19'; 20, 20') being in symmetrical positions with respect to second diametrical planes (p, p') intersecting said central axis and rotated by 45° with respect to said first diametrical planes (π, π'), so that the elastic constant of said elastic member along said second diametrical planes (p, p') is higher than along said first diametrical planes (π, π'), characterized by: - said slots having substantially V-shaped cross sections with vertices radially directed toward said central axis and passing through said first diametrical planes (π,π'); - said elastic member having an outer sheet-like casing and forming with it and with the inner bush a replacement element; - said casing having an outside diameter that is slightly greater than the inner diameter of said outer annular body for interference force-fit therewith. - an outer annular body defining a central axis and adapted to be secured to the frame; - an inner bush coaxial with said outer annular body and adapted to be secured to the transmission of the rotor; - a substantially toroidal elastic member interposed between said outer annular body and said inner bush, said elastic member being made of an elastomeric material having a predetermined elastic constant; wherein said elastic member has two pairs of through slots (19, 19'; 20, 20') substantially parallel to said central axis, the slots (19, 19'; 20, 20') of each pair being diametrically opposite and symmetrical with respect to two first diametrical planes (π, π') intersecting at said central axis; wherein said first diametrical planes (π, π') are orthogonal to each other, said slots (19, 19'; 20, 20') having identical cross sections said slots (19, 19'; 20, 20') being in symmetrical positions with respect to second diametrical planes (p, p') intersecting said central axis and rotated by 45° with respect to said first diametrical planes (π, π'), so that the elastic constant of said elastic member along said second diametrical planes (p, p') is higher than along said first diametrical planes (π, π'), characterized by: wherein said elastic member has two pairs of through slots (19, 19'; 20, 20') substantially parallel to said central axis, the slots (19, 19'; 20, 20') of each pair being diametrically opposite and symmetrical with respect to two first diametrical planes (π, π') intersecting at said central axis; wherein said first diametrical planes (π, π') are orthogonal to each other, said slots (19, 19'; 20, 20') having identical cross sections said slots (19, 19'; 20, 20') being in symmetrical positions with respect to second diametrical planes (p, p') intersecting said central axis and rotated by 45° with respect to said first diametrical planes (π, π'), so that the elastic constant of said elastic member along said second diametrical planes (p, p') is higher than along said first diametrical planes (π, π'), characterized by: - said slots having substantially V-shaped cross sections with vertices radially directed toward said central axis and passing through said first diametrical planes (π,π'); - said elastic member having an outer sheet-like casing and forming with it and with the inner bush a replacement element; - said casing having an outside diameter that is slightly greater than the inner diameter of said outer annular body for interference force-fit therewith.