Upper ocean turbulence and mean current data from the 1997--1998 Surface Heat Budget of the Arctic Ocean (SHEBA) drift in the western Arctic Ocean were used to estimate turbulent shear stress at the ice/ocean interface and hydraulic roughness of the ice undersurface. Techniques for determining interfacial stress from velocity covariance measurements in the ice/ocean boundary layer (IOBL) are complicated by buoyancy flux and the heterogeneity of the ice undersurface, where protrusions corresponding to relatively small upper surface features become major obstacles when compared to the scale of the IOBL. In addition, ice deformation forced relocation of the main SHEBA oceanographic program about midway through the experiment. Hence, there were two different measurement sites to consider. Three different methods were used to compute the undersurface roughness characterizing the undeformed, multiyear floe occupied by the SHEBA project. The first was straightforward (naive) application of the law of the wall to turbulent stress and mean velocity measurements from the turbulence instrument cluster nearest to the interface, assuming a logarithmic velocity profile and constant stress. For the second method, local turbulence closure was used to model the entire IOBL in order to estimate the impact of Coriolis stress attenuation and buoyancy forces on stress and shear near the boundary. A third method, proposed here for the first time, estimated mixing length and eddy viscosity from a scale inversely proportional to the wave number at the peak of the weighted vertical velocity spectrum. The last method appears most robust, in that it shows no overall difference in z0 between the two sites and only minor seasonal and directional differences. The best estimate for the undersurface roughness of undeformed, multiyear ice at the SHEBA site is 0.0048 m < z0 < 0.007, i.e., about 6 mm. Specification of a regional aggregate under-ice roughness requires additional consideration of the added drag from isolated pressure keels and floe edges, along with reduced drag from smoother, newly frozen ice and open water.