The elastic solution for a singularity in an anisotropic trimaterial with perfectly bonded interfaces was obtained in the previous work by Choi and Earmme. The term "trimaterial" denotes an infinite body composed of three dissimilar materials bonded along two parallel interfaces. It is shown in this paper that when the interfaces of an anisotropic trimaterial are one of the following types: (i) perfectly bonded, (ii) rigid, (iii) separated, (iv) separated without slip, and (v) slipping interfaces, the elastic solution for a singularity in the trimaterial has the same form as that for a singularity in a trimaterial with perfectly bonded interfaces, but with the bimaterial matrices properly altered.