Mechanical properties of a composite have been calculated within the pseudopotential method. At calculating the system energy we have taken into account non-harmonic effects, connected with thermal vibrations of atoms, using the quasi-harmonic approximation. For equally deformed states we have obtained a stress-strain dependence. We have calculated elastic modulus, maximum strain and the corresponding maximum strength for LaB6 - MeB2 composite with eutectic composition with regard to the influence of the components’ boundaries, as well as their temperature dependence. There is an exponential dependence of elastic modulus on the composite temperature and in the dependence of elastic modulus - maximum strength ratio on the temperature there is a section where the composite hardening at high temperatures is observed. Different changes in strength and modulus of elasticity depend on the ratio of elastic and total strain of the composite at high temperatures. Accounting of interfacial interaction leads to an increase in the maximum strength of the composite in the whole temperature range, and that provides an increase in the modulus of elasticity.