Caveolae introduce flask-shaped convolutions into the plasma membrane and help to protect the plasma membrane from damage under stretch forces. The protein components that form the bulb of caveolae are increasingly well characterized, but less is known about the contribution of proteins that localize to the constricted neck. Here we make extensive use of multiple CRISPR/Cas9-generated gene knockout and knockin cell lines to investigate the role of Eps15 Homology Domain (EHD) proteins at the neck of caveolae. We show that EHD1, EHD2, and EHD4 are recruited to caveolae. Recruitment of the other EHDs increases markedly when EHD2, which has been previously detected at caveolae, is absent. Construction of knockout cell lines lacking EHDs 1, 2, and 4 confirms this apparent functional redundancy. Two striking sets of phenotypes are observed in EHD1,2,4 knockout cells: (1) the characteristic clustering of caveolae into higher-order assemblies is absent; and (2) when the EHD1,2,4 knockout cells are subjected to prolonged cycles of stretch forces, caveolae are destabilized and the plasma membrane is prone to rupture. Our data identify the first molecular components that act to cluster caveolae into a membrane ultrastructure with the potential to extend stretch-buffering capacity and support a revised model for the function of EHDs at the caveolar neck.