New viscoplastic boundary layer (VPBL) solutions around a flat plate are obtained for viscoplastic fluids in the limiting case of creeping flows with a dominant yield value. Previous studies in the field were mainly heuristic, since only Bingham behavior and no slip at the wall were considered. In fact, in most practical cases, shear-thinning behavior occurs together with slip at the wall. Moreover, together with the yield stress value, these are the main properties which dominate the fields at hand. Due consideration is paid to the permissible stress fields far from the obstacle, and to normalized Cauchy equations introduced in the flowing regions. New similarity solutions are derived for the boundary layer along a flat plate, and the VPBL properties are given in terms of velocity profiles, boundary layer thickness and total drag on the plate. In the case of slip at the wall, a new dimensionless slip parameter psi is introduced. Total drag forces are found to be increasingly smaller when slip and the values of psi increase progressively from zero. For values of psi larger than 1, the material is unyielded and slips with a solid type friction at the wall, after having been cut at the leading edge of the plate. (C) 2004 Elsevier B.V. All rights reserved.