Mass attenuation coefficients (μm2×2μmZeffZeff) for some nonlinear optical materials such as potassium dihydrogen phosphate, ammonium dihydrogen phosphate, zinc tris-thiourea sulphate, and zinc thiourea chloride were measured using a μm2×2μmZeffZeff NaI(Tl) scintillation detector at gamma energies of 122 keV, 356 keV, 511 keV, 662 keV, 840 keV, 1170 keV, 1270 keV, and 1330 keV. In addition, GEANT4 simulations were carried out to mimic the experiment at these energies. As a result, good agreement between the experimental and GEANT4 results was observed. The measured μm2×2μmZeffZeff values were used to compute effective atomic numbers (μm2×2μmZeffZeff) for the selected materials. It was found that the μm2×2μmZeffZeff values were in the range typical for dosimetric materials.