In this paper we are presenting the development of a new concept, the embedded unit cell (EUC) approach, used to calculate local responses in elastic media. In addition, the suggested formulation provides homogenization and multi scale analysis of composite materials, structures and domains; where the classical theory of homogenization does not valid. The EUC approach is based on a multi-scale formulation of the asymptotic homogenization theory to evaluate structure response in several special cases, such as response of non-periodic domains or local/micro response at zones that are expected to develop stress concentrations. The suggested approach is based on the zone-adapted unit cell, restricted by alternative boundary conditions and surrounded by micro scale domain that represents non periodic features of the macroscopic structure. By using the alternative boundary conditions, the periodic assumption of unit cell response that is essential in the classical theory, is no longer required yet preserving an accurate micro-scale response evaluation. This approach offers a reduced computational cost model of the macroscopic/global problem however the precision of the microscale problem solution is retained. The EUC concept broadens the applicability of multiscale analysis techniques, used to evaluate mechanical response of variety of composite materials, in particular highly heterogeneous materials (i.e. concrete, etc.), which are widely used in modern construction industry.