An analysis of buckling for thick anisotropic plates subjected to arbitrary loading is presented. The analysis employs the complex finite strip method which utilizes complex harmonic functions in the longitudinal direction, a cubic polynomial in the transverse direction and a parabolic distribution of the transverse shear strains through the thickness of the thick plate based on the higher-order shear deformation theory. The method is programmed to investigate local buckling of square and long thick plates subjected to compression bending and shear stresses. Examples of the accuracy of the method with an increasing number of strips are presented. The method is then applied to study the local instability of thick orthotropic plates under compression and shear with different boundary conditions. Local instability interaction between compression and shear, and bending and shear in thick orthotropic plates is investigated.