Boundary layer (BL) solutions around a flat plate for viscoplastic fluids are re-examined, after the precursory study by Oldroyd of low inertia Bingham fluid mechanics. Due consideration is paid to the admissible stress fields far from the obstacle. Normalized Cauchy equations are introduced in the flowing regions. They initially contain inertia, pressure, and viscoplastic terms obtained by adding the yield value and a viscous stress excess in the flowing regions. New similarity solutions for the BL along a flat plate are derived, and the VPBL properties are given, in the limiting case of creeping flows with a dominant yield value. Improvements with respect to Oldroyd solution and relevant aspects are presented and discussed.