Abstract The stochastic behaviour of materials and loading is of great importance for buckling and analysis of prestressed beam and frame structures. In this paper, the stochastic stiffness and stress stiffness matrices are developed for stochastic analysis and buckling analysis. The bending rigidity and the buckling load are modelled as stochastic fields. The spectral decomposition known as the Karhunen–Loeve expansion has been used to expand the random fields. Using the Karhunen–Loeve expansion, the stiffness and stress stiffness closed-form matrices are formulated in terms of discrete parameters. The matrices are developed considering both classical Euler–Bernoulli theory and Timoshenko beam theory. Two case studies involving a pinned-pinned column and a frame structure is used to demonstrate the effectiveness of the proposed methods.