The behaviour of steel plates and reinforced concrete slabs which undergo large deflections has been investigated using the finite element method. Geometric and material nonlinearities are both considered in the study. Two computer programs have been developed for the analysis of plates and slabs. Ihe first program is for the elastic stability of plates. The elastic buckling loads obtained for plates with and without openings and under different edge loading conditions have been compared with the analytical and numerical results obtained by other investigators using different techniques of analyses. Good correlation between the results obtained and those given by others has been achieved. Improvements in the accuracy of the results and the efficiency of the analysis for plates with openings have been achieved. The second program is for the full range analysis of steel plates and reinforced concrete slabs up to collapse. The analysis can trace the load-deflection response up to collapse including snap-through behaviours. The program allows for the yielding of steel and the cracking and crushing of concrete. The modified Newton-Raphson with load control and displacement control methods is used to trace the structural response up to collapse. The line search technique has been included to improve the rate of convergence in the analysis of reinforced concrete slabs. The program has been tested against experimental and numerical results obatined by other investigators and has been shown to give good agreement. The accuracy of a number of integration rules usually adopted in nonlinear finite elecent analyses to evaluate the stress resultants from the stress distribution throughout concrete sections has been investigated. A new integration rule has been proposed for the integration of stress distributions through cracked concrete sections or cracked and crushed concrete sections.