Electron multipacting in a 2.8‐GHz TM010‐mode anodized niobium test cavity at 1.4 K has been studied experimentally. An electron multipactor simulation computer program, which we developed, successfully calculates the multipactor field levels and multipactor location observed experimentally and also provides additional details of the multipactor phenomena. With the multipactor simulation program, a sharp‐cornered TM010‐mode cavity has been designed in which multipacting is greatly reduced. A subsequent experiment on such a sharp‐cornered anodized niobium cavity has shown that electron multipacting is in fact eliminated for this cavity up through the highest field achieved. This work has shown that, with a simple modification in geometry, multipacting can probably be eliminated in the superconducting structure for the Stanford electron accelerator.