AbstractA meshless local Petrov–Galerkin (MLPG) method is applied to solve static and dynamic problems of orthotropic plates described by the Reissner–Mindlin theory. Analysis of a thick orthotropic plate resting on the Winkler elastic foundation is given too. A weak formulation for the set of governing equations in the Reissner–Mindlin theory with a unit test function is transformed into local integral equations on local subdomains in the mean surface of the plate. Nodal points are randomly spread on the surface of the plate and each node is surrounded by a circular subdomain to which local integral equations are applied. The meshless approximation based on the Moving Least–Squares (MLS) method is employed in the numerical implementation. The present computational method is applicable also to plates with varying thickness. Numerical results for simply supported and clamped plates are presented. Copyright © 2006 John Wiley & Sons, Ltd.