In the case of existing in free-edge delaminations of composite laminates which are symmetry with respect to mid-plane in laminates also, in the case of asymmetry and anti-symmetry, the generalized quasi-three dimensional displacement field equations developed from quasi-three dimensional displacement field equations can be applied to solve above cases. We introduce three paramenters in this paper, which have not been used in quasi-three dimensional displacement field equations until now. To the laminate subjected to the axial extension strain $varepsilon$0(C1) in $chi$-direction, the bending deformation $chi$$chi$(C$_2$) around у-direction, the bending deformation w$chi$(C$_4$) around z-direction and the twisting deformation $chi$$chi$y(C$_3$) around $chi$-direction .The generalized quasi-three dimensional displacement field equations are able to be analyzed efectively.