The measured the two-photon absorption (TPA) cross sections of ethanol solution of trans-stilbene and its two substitutes excited by nanosecond radiation of the 2nd harmonic of a Nd:YAG laser (532nm) are presented. To determine the TPA cross section, a method based on measurements of photochemical decomposition of molecules of the examined compounds having low photostability is suggested. The measured value of the TPA cross section of trans-stilbene in ethanol is found to be 25GM, and the TPA cross sections of the trans-stilbene substitutes are found to be 60 and 70GM. The TPA cross section of trans-stilbene substitutes obtained in the present paper is compared with the experimental and theoretical data obtained by other authors. The results of investigations demonstrate that the photochemical decomposition method can be successfully used to determine experimentally the two-photon absorption cross section of the compounds unstable under photoexcitation, including photochromatic molecules, biological objects, and radical photoinitiators.