The Dancoff correction has an important role in the calculation of the resonance escape probability of water moderated lattices. By use of the method of Dancoff and Ginsburg, it is shown how to take account of the shadowing of distant neighbors by near neighbors. Although these results are in good agreement with Monte Carlo calculations, the method is very complicated and laborious. A new approximate analytical formula for the Dancoff correction is developed which is much simpler and which gives good agreement with the Monte Carlo results.