Using the Fourier transformation method,we accurately solved the Gauss Model with long-range interactions on the d-dimensional hyper-cubic lattices and the two-dimensional triangular lattices.The long-range interactions we considered here include power exponential decreasing,exponential decreasing and natural logarithmic decreasing.At the same time the critical behavior of the Gauss Model with long-range interactions decaying as r-α on two-dimensional triangular lattices is studied.The critical points of the system under these circumstances are calculated.According to the results we have obtained,we can easily compare the effect of different types of long-range interactions on the critical behavior of the system.As will be seen,for the existence of long-range interactions,the critical temperature of the system rises to some extent.And the effect of the long-range interaction on the critical temperature depends on its decaying rate.