AbstractThis paper surveys some of the fundamental properties of symplectic integration schemes for classical mechanics and particle methods in particular. The widely used Störmer‐Verlet method is discussed in detail and implications of conservation of symplecticity on long term simulations are outlined. The second part of the paper describes the application of a Lagrangian particle method and the Störmer‐Verlet time integrator to numerical weather prediction (NWP). A simple vertical slice model and non‐hydrostatic flow over orography are discussed in detail. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)