Smoothed particle hydrodynamics is extended to a normalized, staggered particle formulation with boundary conditions. A companion set of interpolation points is introduced that carry the stress, velocity gradient, and other derived field variables. The method is stable, linearly consistent, and has an explicit treatment of boundary conditions. Also, a new method for finding neighbours is introduced which selects a minimal and robust set and is insensitive to anisotropy in the particle arrangement. Test problems show that these improvements lead to increased accuracy and stability. Published in 2000 by John Wiley & Sons, Ltd.