<p>A theoretical investigation into the effectiveness of a plate thickness against the ultimate strength of a compressed slabs and box girders is carried out. Series of the buckling analyses, the elastic, the viscoplastic and the ultimate strength are performed by the rheological-dynamical inelastic theory and the finite strip method on a slabs and box girders under thrust. In the analytical method, rheological-dynamical analogy (RDA) is introduced to express the critical stresses of slabs and box girders in the range of viscoplastic strains and strain hardening. Applying the finite strip method (FSM) as a semi-analytical method, the fundamental equilibrium equations are derived based on the principle of minimum total potential energy. Apart from the quantitative research the qualitative research is presented to demonstrate the capabilities of the present theory.</p>