In this study a numerical approach to simulate elastic behavior of lightweight concrete, is presented, at mesoscopic level. Concrete is considered as a bi-phasic material, composed of a granular skeleton dispersed in a mortar. Aggregates generation should respect a granular model where a maximum distance between aggregates is imposed. The granular media is also defined by a granular curve and a compacity. A numerical concrete sample is carried out, using three-dimensional finite element mesh. Here lightweight concretes are considered, where Young's modulus of natural sand based mortar is higher than the modulus of the lightweight coarse aggregates. Different concretes are carried out, according to experimental studies from literature, in order to distinguish the influence of Young's modulus contrast, and of the concrete compacity, on mechanical behavior. Then numerical compressive tests are realized until an experimental value of compressive strength, and the local stress and strain distribution around aggregates is studied, still remaining in the elastic domain. According to these results, breaking of this kind of concrete occurs when the maximum strain is reached in the lightweight aggregates surrounded mortar.