We present an analytical and numerical study of the possibility of existence of surface localized modes, the so-called Tamm states, in a one-dimensional (1D) comb-like phononic crystal (PnC). The structure is made out of periodic array of stubs of lengths d2grafted along a waveguide and separated from each other by a tube of length d1. We show the existence of surface modes for the semi-infinite structure. In particular, when one considers two complementary semi-infinite systems obtained by cutting the infinite one into two parts, we obtain one surface mode per gap induced by the surface of the two complementary systems. Furthermore, we demonstrate that these surface modes can be detected from the maxima and minima of the transmission spectrum, when the finite structure is grafted vertically along a homogeneous acoustic waveguide. That means that one can observe experimentally this type of modes for acoustic waves in slender tubes. These results may find many practical applications in noise control and highly sensitive PnC sensors. © 2021 Elsevier Ltd. All rights reserved.