Motivated by the Galileo observations of asteroid-associated perturbations of the solar wind magnetic field, we have conducted analytical and numerical studies on the solar wind interaction with an asteroid. As asteroid dimensions are small compared with solar wind ion scale lengths, the interaction cannot be described in terms of magnetohydrodynamic (MHD) theory. We have obtained the solutions for the whistler mode mediated standing waves for the asteroid wake in a general geometry. The wake wave may contain many magnetic field rotations. In the special geometry with the interplanetary field perpendicular to the solar wind flow velocity, the constant phase lines for the wake wave are parabolic. Our analytical analysis and numerical simulations show that nonlinear effects do not modify the linear theory significantly even when the perturbed field is of the order of the background field. Magnetohydrodynamic shock waves are absent in the interaction of solar wind with the small object. Kinetic effects for a &bgr;=1 plasma modify the wake wave only slightly by damping the short wavelength waves. Numerical simulations also show that the interaction of the solar wind with a small dipole field forms a draped magnetic field structure similar to that observed by Galileo during the encounter with the asteroid Gaspra. ¿ American Geophysical Union 1996