Elastic anti-vibration isolation apparatus with integrated hydraulic damping, consisting of a thick conical membrane of elastomer compound bonded to internal and external rigid frames, and crimped in a casing containing a damping liquid, characterized by the fact that the rigid partition which separates the variable volume chamber from the expansion space has a passage for the damping liquid realized in one or two parts, the dimensions of which can be adjusted by grinding or lathe-working at least one of the components, base or cover, of the rigid partition, or by the insertion of shims between the constituent parts, thereby making it possible, using a set of similar components, to realize a range of elastic mountings with damping characteristics adapted to desired utilization frequencies.