A contact discontinuity in a collision-free magnetized plasma is a thin layer, possessing a nontrivial magnetic structure, across which no net plasma flow takes place (&ngr;n=0) even though the magnetic field has a nonvanishing component (Bn≠0) normal to it. This paper examines the structure of such discontinuities in a simple plasma model consisting of two oppositely directed cold ion beams and a background of cold massless electrons such that exact charge neutrality is maintained so that the electric field E≡0. The basic equations describing self-consistent equilibria are developed for the more general situation where a net flow across the layer takes place (&ngr;n=0) and where the magnetic field has two nonzero tangential components By and Bz but where E remains zero. These equations are then specialized to the case &eegr;n≡0, Bz≡0, and four different classes of sheets are obtained, all having thickness of the order of the ion inertial length: (1) layers separating two identical plasma and magnetic field regions. (2) an infinite array of parallel layers producing an undulated magnetic field, (3) layers containing trapped ions in closed orbits which separate two vacuum regions with uniform identical magnetic fields, and (4) layers which reflect a single plasma beam, leaving a vacuum with a revesed and compressed tangential field on the other side. Solutions for which &ngr;n=0 but Bz≠0 may also exist but have not been analyzed; rotational discontinuities are shown not to be possible in this model.