The paper presents a numerical technique based on improved finite differencc formulae of the Hermitian type, for the analysis of structures taking into account the second-order effects of the displacements of the structure. The same method can be extended
to evaluate the critical loads of structures. The method, which is quite general, does not make use of previously tabulated data and can also include non-linear effects in the analysis. It can be applied to the second-order analysis of most plane structures
including continuous beam-columns, multi-storeyed rigid frames and arches. The author has illustrated the approach with several applications.