The well-known problems of significant disagreements between partial photoneutron reactions ( γ , n ), ( γ ,2 n ) and ( γ ,3 n ) cross sections data obtained in various experiments are discussed. Using new objective criteria of data reliability it was shown that majority of data under discussion contains significant distortions because of definite shortcomings of experimental photoneutron multiplicity sorting methods used – the majority of experimental data obtained such methods are not reliable. These criteria were transitional photoneutron multiplicity functions F i = σ ( γ ,in)/ σ ( γ , x n) having values not higher than 1.00, 0.50, 0.33, 0.25, 0.20…., correspondingly for i = 1, 2, 3, 4, 5,…New experimentally-theoretical method was proposed to evaluate reliable data free from shortcomings of neutron multiplicity sorting. For partial reaction cross section evaluation the only experimental data for total neutron yield reaction cross section σ exp ( γ , x n) = σ exp [( γ ,n) + 2( γ ,2n) + 3( γ ,3n) + …] free from the mentioned shortcomings are used together with functions F i theor calculated within the modern model for photonuclear reactions − σ eval ( γ ,in) = F i theor · σ exp ( γ ,xn). Many new reliable data for 90 Zr, 115 In, 112,114,116,117,118,119,120,122,124 Sn, 159 Tb, 181 Ta, 197 Au, and 208 Pb were evaluated. Deviations of evaluated data from experimental ones are analysed and the physical consequences are discussed.