Abstract: The formula of a J integral presented by J.R.Rice is extended to problem of 2 D variable thickness plates.The extended J integral formula is derived in terms of the path independent.Then the integral conservation is verified by using finite element method.At last,the calculation results for some variable thickness plates made of photoelastic material are compared with their photoelastic test data,and the differences between them are less than 4%.It is proved that the extended J integral formula for the 2 D variable thickness plates is path independent and can be taken as a fracture pamarater for damage tolerance analysis.Furtheremore,this integral can be solved numerically by using 2 D general finite element programs.It is therefore of practical value for the fracture analysis of Ⅰ mode cracked plate with thickness which does not vary too mueh.