FAM134B/RETREG1 is a selective ER-phagy receptor that regulates the size and shape of the endoplasmic reticulum. The structure of its reticulon-homology domain (RHD), an element shared with other ER-shaping proteins, and the mechanism of membrane shaping remain poorly understood. Using molecular modeling and molecular dynamics (MD) simulations, we assemble a structural model for the RHD of FAM134B. Through MD simulations of FAM134B in flat and curved membranes, we relate the dynamic RHD structure with its two wedge-shaped transmembrane helical hairpins and two amphipathic helices to FAM134B functions in membrane-curvature induction and curvature-mediated protein sorting. FAM134B clustering, as expected to occur in autophagic puncta, amplifies the membrane-shaping effects. Electron microscopy of in vitro liposome remodeling experiments support the membrane remodeling functions of the different RHD structural elements. Disruption of the RHD structure affects selective autophagy flux and leads to disease states.