Finite strip methods are presented for the prediction of buckling stresses and natural frequencies of vibration of “long” prismatic plate structures which may be formed of fibre-reinforced, composite, laminated material with very general properties. The finite strip methods are of the single-term type with complex algebra employed to accommodate applied in-plane shear stress and anisotropic material behaviour. The developments, described here follow on very directly from an earlier paper in this Journal ([1] Dawe and Craig, Int. J. Mech. Sci. 30, 77, 1988) to which frequent reference is made herein. The first development is the introduction of major improvements and extensions on the earlier work [1] which is based upon the use of first-order shear deformation plate theory to represent the out-of-plane properties of plate flats: the chief advance involves the use of multi-level substructuring procedures, including the introduction of so-called superstrips, but eccentric connections of component plates at their junctions is also included. The second development is the introduction of a new finite strip analysis which is based on the use of classical plate theory and which is complementary to the shear deformation analysis, with similar advanced features. Two computer programs, BAVPAS and BAVPAC, are introduced and description is given of some results of the application of these programs.