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The paper considers a mathematical model which is used to study a composite material similar in structure to asphalt concrete and it takes into account presence of solid particles of different sizes and a soft and plastic binder. The twodimensional method of discrete elements has been applied to investigate destruction of asphalt-concrete samples under uniaxial compression, tension during splitting and compression by the Marshall method. The numerical model takes into account presence of large particles of rubble, asphalt mastic filling rubble pores and sticky (capable of recovering after rupture) communication between rubble particles. The force interaction between various components of the asphalt concrete has been described with the help of elastic repulsion between rubble particles, friction force and force responsible for sticking of particles due to presence of a binder. This model gives a correct fracture pattern for uniaxial compression, stretching during splitting and compression according to the Marshall method and this pattern coincides with the real experiment. It is the correct picture of destruction for three different schemes of material loading which makes it possible to assess the adequacy of the mathematical model which has been used. Basic physico mechanical characteristics of the binder which determine strength and deformability of asphalt concrete have been established in the paper. It has been shown that for an adequate description of physico mechanical characteristics for asphalt concrete it is necessary to study and measure properties of an asphalt binder that is a mixture of bitumen and fine mineral filler which determines parameters of interaction between rubble particles. The numerical experiments serve as a basis and make it possible to propose new laboratory methods for testing a mixture of stone materials and organic binders which are much simpler and, therefore, cheaper than standard tests on asphalt concrete. In addition these tests will more accurately predict behavior of asphalt concrete in real conditions.