We investigate the aspects of surface defects in a new class of 4d N=1 superconformal quiver theories named class S_k. As the first step, we focus on the construction of the surface defects in IR under the situation where the UV theories of class S_k are higgsed by giving the vevs to some fields and try to specify them as 2d N=(0,2) vortex string theories by computing its elliptic genera encoded in the IR description of the superconformal indices of class S_k. This picture is consistent with type IIA brane construction of the vortex strings. Another way to argue the surface defects is to see their actions on the superconformal indices as difference operators, and we would like to discuss whether such difference operators form the algebras labelled by the representations of SU(N) flavor symmetries.