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Axion-like particles $a$ (ALPs) that couple to the Standard Model (SM) gaugefields could be observed in the high-energy photon scattering $\gamma N\to N a$off nuclei followed by the $a\to \gamma\gamma$ decay. In the present paper wedescribe the calculation of the ALP production cross-section and the propertiesof this production. The cross section formulas are implemented in the programfor the simulation of events in the NA64 experiment, the active electron beamdump facility at the CERN SPS. We study the prospects of the NA64 experiment tosearch for ALP in the $10\, \mbox{MeV} \lesssim m_a\lesssim 100$ MeV mass rangefor the statistics corresponding to up to $5\times 10^{12}$ electrons on target(EOT).

Photoproduction of axion-like particles in the NA64 experiment