Abstract: Based on two-dimensional displacement field of cracked plate in the linear elastic fracture mechanics, mathematical expression with unknown function of three-dimensional displacement field is given in variable separating type. Then three-dimensional strain field and stress field are obtained. By means of equations of geometry and physics, the governing equations and boundary conditions of above unknown displacement function are formulated using variational method on the foundation of principle of virtual displacement. The dis-placement functions are solved by the above method. Three-dimensional effect analysis of cracked plate is conducted by the model of equivalent plane strain and equivalent plane stress sections and the theoretical formulas on the relation be-tween fracture toughness and plate thickness are determined. Two kinds of test materials, LY12CZ(L-T) and TC4(L-T), are used to verify theoretical equation.

Key words: Fracture toughness, Principle of virtual displacement, Thickness effect, Variable separating solution