We aim to obtain a consistent description of non-thermal emissions from Abell 2256 and to give a prediction for a gammaray emission from this galaxy cluster. Assuming that a radio relic illuminates a localization of an ongoing merger, and that both radio and non-thermal part of hard X-ray emission are due to electron component of cosmic rays filling the relic, we derived from radio and hard X-ray properties of the relic in A2256 the magnetic field strength and number densities for relativistic electrons and protons. Due to the interpretation of the radio relic as a structure formed just where a shock front is, we discuss a gamma-ray emission at the cluster periphery. The estimated strength of the magnetic field in the relic is equal to 0.05 ΞΌG, while the amplitude of the electron number density varies from 3Γ10 -4 to 3Γ10 -5 cm -3 (respectively for the relic thickness of 50 to 500 kpc). We got a substantial degree of non-equipartition between cosmic rays and magnetic field in the relic region, where the CR pressure is approaching that of thermal gas. Our prediction for LOFAR is a synchrotron flux from the relic region of the order of βΌ6 Jy at 60MHz and βΌ10 Jy at 30MHz. The lower limit of the Ξ³-ray flux from the relic region calculated for a hadronic channel is of the order of 10 -12 erg cm -2 .