Abstract We report observations of the Apollo-class potentially hazardous asteroid 1981 Midas, which passed 0.090 au from Earth (35 lunar distances) on 2018 March 21. During this close approach, Midas was observed by radar both from the Arecibo Observatory on March 21 through 25 (five nights) and from NASA’s Goldstone Deep Space Communications Complex on March 19 and 21. Optical lightcurves were obtained by other observers during four apparitions (1987, 1992, 2004, and 2018), which showed a rotation period of 5.22 hr. By combining the lightcurves and radar data, we have constructed a shape model for Midas. This model shows that Midas has two lobes separated by a neck, which, at its thinnest point, is about 60% of the width of the largest lobe. We also confirm the lightcurve-derived rotation period and show that Midas has a pole direction within 6° of ecliptic longitude and latitude (λ, β) = (39°, −60°) and dimensions of (3.41 ± 9%) × (1.90 ± 11%) × (1.27 ± 29%) km. Analysis of gravitational slopes on Midas indicates that nearly all of the surface has a slope less than the typical angle of repose for granular materials, so it does not require cohesion to maintain its shape. In addition, we measured a circular polarization ratio of 0.83 ± 0.04 at Arecibo’s 13 cm wavelength, which is the highest seen to date for any near-Earth asteroid with visible and near-infrared spectral type V.