An affine factorable surface of the second kind in the three dimensional pseudo-Galilean
is studied depending on the invariant theory and theory of differential equation. The rst and
second fundamental forms, Gaussian curvature and mean curvature of the meant surface are obtained
according to the basic principles of differential geometry. Also, some special cases are presented by
changing the partial differential equation into the ordinary differential equation to simplify the solving
process. The classication theorems of the considered surface with zero and non zero Gaussian and
mean curvatures are given. Some examples of such a study are provided.