The main objective of the current thesis is to develop and verify a simple technique which is able to introduce heterogeneity in the constitutive models of solids and investigate the mechanical behaviour at low strain rates. By adopting simple constitutive models which are computationally inexpensive the aim is to capture effects of spatial variation of materials properties, geometric variation effects such as void distribution and interaction and thus being able to capture fracture and failure. In addition, important aspects are being able to predict realistic paths for the onset and evolution of damage as well as material size effects. Such techniques will be applied in order to predict experiments in various kind of materials including foams, composites. The technique developed in the current thesis involves introduction of material heterogeneity at the micro-level using the finite element method. Distribution of material properties and geometric fields are numerically generated based on probability density functions. FE models are generated by manipulating the input file via a FORTRAN program. A Monte Carlo type analysis is performed in ABAQUS where the stochastic volume element (SVE) generated, is solved deterministically using ABAQUS implicit solver. The process is repeated N times in order to obtain the scatter and the mean of the macroscopic response. Mesh convergence studies as well as sensitivity of the size of the number of cells is conducted. Following this approach numerical modelling of four types of materials are studied; a sintered titanium solid with 0.95 relative density; a polycrystalline elasto-plastic solid; a low porosity elasto-palstic solid with relative densities in the range 0.70-0.99 and a cellular elasto-plastic solid with relative densities in the range 0.37-0.48. Predictions are compared to previously numerical studies as well as to experiments. For all materials examined, the heterogeneous approach proved to capture the mechanical behavior of materials at no additional computational cost