Exact three-dimensional elasticity solutions for some static and dynamic problems of bending multi-layered anisotropic rectangular plates are presented. They are derived by the method of initial functions without employing any hypotheses about the character of the stress-strain state of the linearly elastic anisotropic structures. Two computationally stable algorithms of the method which extend the field of its application are developed. The results presented illustrate some possibilities of the designed stable algorithms. The analysis of multi-layered plates under concentrated static and harmonic dynamic loads are presented. (C) 1998 Elsevier Science Ltd. All rights reserved.