By using the dilational strain energy density on the elastic-plastic boundary at crack front, the hydrostatic tension stress on the constant strain energy density plane around crack-tip and the plastic area size near crack-tip as the parameters, three fracture initiation criteria of mixed-mode surface crack are proposed under the small-scale yielding condition in this paper. The general mathematical expressions of the initiation angles ( α ∗ i, θ ∗ i ) and the critical loads θ ∗ i at the arbitrary points of the semi-elliptical surface inclined crack are given. The initiation angles ( α ∗ i, θ ∗ i ) and the critical loads θ ∗ i of LC4CS finite width plate with a semi-elliptical surface inclined crack under uniform tension are calculated when the location angle φ is equal to 0°, 15°, 30°, 45°, 60°, 75° and 90°, and the inclined angle β is equal to 15°, 30°, 45°, 60°, 75° and 90° respectively. The curves θ ∗ i-β, θ ∗ i-φ, √aθ ∗ i WBK Ie -φ and √aθ ∗ i WBK Ie -β are plotted. The calculated results are discussed and compared with the results in the paper by Chen Xiao-Ming et at. [in Engng Fracture Mech., Vol. 24, pp. 127–144 (1986)] which are from the [ G] max criterion, [ S] min criterion, [ σ gq ] max criterion and experiments. It has been found that three criteria proposed in this paper are more practicable than the [ G] max criterion, [ S] min criterion and [ σ gq ] max criterion.