Context. Several circumbinary planets have recently been discovered. The orbit of a planet around a binary stellar system poses several dynamic constraints. In addition to these constraints, the effects that radiation from the host stars may have on the planet atmospheres must be considered. We here evaluate these effects. Because of the configuration of a close binary system, these stars have a high rotation rate, even for old stars. The fast rotation of close, tidally locked binaries causes a permanent state of high stellar activity and copious XUV radiation. The accumulated effects are stronger than for normal exoplanets around single stars and cause a faster evaporation of their atmospheres. Aims. We evaluate the effects that stellar radiation has on the evaporation of exoplanets around binary systems and on the survival of these planets. Methods. We considered the X-ray and EUV spectral ranges (XUV, 1-912 Å) to account for the photons that are easily absorbed by a planet atmosphere that is mainly composed of hydrogen. A more complex atmospheric composition is expected to absorb this radiation more efficiently. We used direct X-ray observations to evaluate the energy in the X-rays range and coronal models to calculate the (nondetectable) EUV part of the spectrum. Results. We considered in this problem different configurations of stellar masses, and a resonance of 4:1 and 3:1. The simulations show that exoplanets orbiting close binary systems in a close orbit will suffer strong photoevaporation that may cause a total loss of atmosphere in a short time. We also applied our models to the best real example, Kepler-47 b, to estimate the current mass-loss rates in circumbinary planets and the accumulated effects over the time. Conclusions. A binary system of two solar-like stars will be highly efficient in evaporating the atmosphere of the planet (less than 6 Gyr in our case). These systems will be difficult to find, even if they are dynamically stable. Still, planets may orbit around binary systems of low mass stars for wider orbits. Currently known circumbinary planets are not substantially affected by thermal photoevaporation processes, unless Kepler-47 b has an inflated atmosphere. The distribution of the orbital periods of circumbinary planets is shifted to much longer periods than the average of Kepler planets, which supports a scenario of strong photoevaporation in close-in circumbinary planets.