  In this paper, we study the problem of finding the affine factorable surfaces
in a 3-dimensional isotropic space with prescribed Gaussian (K) and mean (H)
curvature. Because the absolute figure two different types of these surfaces
appear by permutation of coordinates. We firstly classify the affine factorable
surfaces of type 1 with K,H constants. Afterwards, we provide the affine
factorable surfaces of type 2 with K=const. and H=0. In addition, in a
particular case, the affine factorable surfaces of type 2 with H=const. were
obtained.
