This paper presents the numerical modelling of the experimental determination of the compressive strength and the static modulus of elasticity of the lightweight concrete using the finite element method (FEM). In the theoretical review, a concrete damage plasticity (CDP) model of the concrete behaviour is described. Numerical modelling and nonlinear static (incremental-iterative) analyses were performed for two different configurations using the Abaqus© software. The first configuration of the model considers the experimental determination of the concrete compressive strength of the concrete cube, and the second one the determination of the static modulus of elasticity on the concrete cylinder. Steel plates in the three-dimensional FEM models located on the upper and lower sides of the specimens, which serve as the support or for the load application, thus capturing the contact conditions of concrete specimens with testing equipment more realistically, have also been taken into account.