In this contribution, a mesomechanical approach to simulate the mechanical behavior with explicit consideration of the three-dimensional structure is applied to study the elasto-plastic response of a metal matrix composite material under tension. A procedure of a step-by-step packing (SSP) of a finite volume with structural elements has been used to design the composite structure consisting of an Al(6061)-matrix with Al2O3-inclusions. A three-dimensional mechanical problem of the structure behavior under tension has been solved numerically, using both an implicit finite-element method and an explicit finite-difference code. Special attention is given to the comparison of quasistatic and dynamic calculations. Evolution of plastic deformation in the matrix during tensile loading has been investigated. Qualitative and quantitative analysis of different components of stress and strain tensors is provided on the basis of mesomechanical concepts. Basing on the 3D-analysis, some conclusions regarding an applicability of a 2D approximation when considering deformation behavior on meso and macro scale levels have been done.