In this paper we present some results from the application of a mesh-free method introduced previously (Compos Struct 2011;93:3112–9 and 94:84–91) for bending analysis of laminated composite plates. This method is applicable to a wide range of bending problems without limitation in the stacking sequence of the laminated plates and the boundary conditions. Herein, two specific types of problems, having traction free boundaries, are examined and the issues related to the solution of them are addressed. Also as new benchmark problems, some more results for cross-ply and angle-ply composites are presented.