The probability of direct excitation of excitonic molecule in the two-photo
n absorption process is calculated with an Hylleraas-Ore type biexciton env
elope, which is variationally optimized. In the second order of perturbatio
n, because of the resonance effect, only the exciton Gamma (5) intermediate
state is taken into account. The band structure at band extrema due to spi
n-orbit interaction is assumed. The transition probability of two-photon ab
sorption is expressed by matrix element between the free exciton and the bi
exciton envelopes. The obtained probability of two-photon absorption in CuC
l is about three orders of magnitude smaller when compared to that obtained
by Hanamura.