The lattice Green's function for the simple cubic lattice ( γ = 1) and tetragonal lattice at an arbitrary point ( l, m, n) I(a;l,m,n;γ) = 1 π 3 ∫∫ ∫ o π coslx cosmy cosnx a−iϵ−γ cosx− cos y− cosx dxdydz is evaluated, assuming a ⩾ 0, γ ⩾ 0 without loss of generality. The integral I( a; l, m, n; γ) which has singularities at a = ± γ ± 1 ± 1, is expressed in all regions of ( a, γ), i.e., for (i) a > 2 + γ, (ii) 2 − γ > a > γ( γ < 2), (iii) a < γ − 2 ( γ > 2), (iv) a < 2 − γ (1 < γ < 2) and γ > a (0 < γ < 1), (v) | a − γ| < 2 and a + γ > 2, in terms of Kampé de Fériet function by the method of the analytic continuation using the Mellin-Barnes type integral. The numerical values are shown in figures. The high temperature susceptibilities of the Heisenberg model of the ferro- and antiferromagnets are calculated using the results of I( a; l, m, n; γ), showing a shift from three to two dimensions and that from three to one dimensions. The correlation function of the isotropic ferromagnet is calculated and the critical index ν is observed to be 1.