Support ring assembly for tires comprising a rigid ring of I-shaped cross-section having an outer diameter less than the inner diameter of the tire tread when the tire is under load and having an inner diameter greater than the outer diameter of the cylindrical wheel rim is improved due to the fact that the assembly further comprises at least one solid annular part of elastic material which is mountable between the rim and the rigid ring, the annular part having an outer diameter substantially equal to the inner diameter of the rigid ring and having an inner diameter and width such that after the tire has been mounted on the rim, the fastening of the assembly on the rim is assured by compression of the elastic material of the annular part.