Many structural parts are exposed to high temperatures and loading. It is then important to have data about material inelastic behaviour under such exploiting conditions. Influence of temperature on mechanical characteristics of a material may be inserted via the creep coefficient in the range of visco-elasto-plastic (VEP) strains. This damage parameter is implemented in this paper in conjunction with mathematical material modelling approach named rheological-dynamical analogy (RDA) in order to address structural stiffness reduction due to inelastic material behaviour. The aim of this paper is to define structural-material internal damping based on both the RDA dynamic modulus and modal damping ratio, by modelling critically damped dynamic systems in the steady-state response. These systems are credible base for explanation of the phenomenon of thermo-visco-plasticity and creep in structural-material response due to high temperatures and loading. Though elastic buckling information for folded-plate structures is not a direct predictor of capacity or collapse behaviour on its own, both the mode and the load (moment) are important proxies for the actual behaviour. In current design codes, such as AISI S100, New Zealand/Australia, and European Union, the design formulae are calibrated through the calculation of elastic critical buckling loads (or moments) to predict the ultimate strength, thus the ability to calculate the associated elastic buckling loads (or moments) has great importance. Moreover, the buckling mode shapes are commonly employed into non-linear collapse modelling as initial geometric imperfections and thermal performance of folded-plate structures in fire. To examine the buckling behaviour of folded-plate structures, the main numerical solution methods are used such as the finite element method (FEM) and finite strip method (FSM). This paper aims at providing a unified frame for quasi-static inelastic buckling and thermal loading of uniformly compressed folded-plate structures using the FSM.