The core of this thesis lies in the micropolar (Cosserats’) theory of elasticity, developed as one of the possible generalisations of the classical (Cauchy’s) theory, in order to describe the behaviour of heterogeneous materials with a pronounced internal structure (microstructure), which the classical theory neglects. In addition to the standard displacement field, an additional independent microrotation field exists in the micropolar theory due to the consideration of the microstructure of the material, and to completely describe the behaviour of a linear-elastic isotropic and centrosymmetric micropolar material, the values of six micropolar material parameters must be known. However, due to the lack of a reliable and accepted methodology for their determination, the theory is still not widely applied in practice. Therefore, this research is conducted through two major phases in order to somehow contribute to the development of the necessary methodology. In the first part, a new family of finite elements of arbitrary order for the linear analysis of the micropolar continuum is presented, where the displacement field is interpolated by enhanced fixed-pole interpolation which arose from an investigated correlation between known interpolation schemes, originating from the analysis of geometrically exact 3D beams, highlighting here interpolations on Lie groups SE (3) – helicoidal interpolation and SR (6) – fixed-pole interpolation, in their linearised form, with a linked interpolation. The enhanced fixed-pole interpolation derived from this observed relationship represents a possible interpretation of the linked interpolation, which is widely used in the linear analysis of the Timoshenko beam, but is not sufficiently explored in the general micropolar continuum theory. Static and vibrational analyses of the micropolar continuum are conducted through several numerical examples, demonstrating improved efficiency of the newly developed finite elements compared to conventional elements. In the second part, the newly developed finite elements are used for the identification of micropolar material parameters by inverse analysis based on two specific experiments. The first experiment involved a four-point bending virtual experiment on perforated specimens, where the value of the coupling number, as one of the two existing micropolar parameters in 2D, is determined by inverse analysis. The second example investigates the discrepancy between the theoretically predicted stress concentration factor around a circular hole in a plate subjected to uniaxial tension and the experimental results. In pursuit of improved theoretical predictions, the application of micropolar theory is explored and a detailed methodology based on parametric and inverse analysis is presented for this purpose. However, it is demonstrated that there is no unique combination of micropolar parameters that simulates the experimental results for all tested specimens, and based on the conducted analysis, we indeed affirm that the micropolar theory is not suitable for materials with a very low-scale internal structure and can not predict the obtained experimental results.