Rice has proposed a simplified method for estimating the J-integral for a CCT specimen. Ohji has also suggested a simplified method of estimating the J-integral for the same specimen. These J estimation formulas have been derived based on the assumption of a deep crack. In this study, the applicable range of these J estimation formulas is analytically studied for four materials ; linear elastic, rigid perfectly-plastic, elastic perfectly-plastic and elastic-plastic. The necessity of a deep crack for these J estimation formulas is also studied analytically for a strain hardening plastic material for L/W>3 when a load-point displacement is used. Results show that these formulas are valid for any 2a/W for three materials ; linear elastic, rigid perfectly-plastic and elastic perfectly-plastic, and that the use of a mouth opening displacement is superior to the use of a load-point displacement in the applicable range. Results also show that a deep crack must be assumed for n≲3 when L/W=4. Based on the results, we can conclude that a mouth opening displacement should be used for estimating the J-integral for a CCT specimen.