Lattice structure and symmetry of two-dimensional (2D) layered materials are of key importance to their fundamental mechanical, thermal, electronic and optical properties. Raman spectroscopy, as a convenient and nondestructive tool, however has its limitations on identifying all symmetry allowing Raman modes and determining the corresponding crystal structure of 2D layered materials with high symmetry like graphene and MoS2. Due to lower structural symmetry and extraordinary weak interlayer coupling of ReS2, we successfully identified all 18 first-order Raman active modes for bulk and monolayer ReS2. Without van der Waals (vdW) correction, our local density approximation (LDA) calculations successfully reproduce all the Raman modes. Our calculations also suggest no surface reconstruction effect and the absence of low frequency rigid-layer Raman modes below 100 cm-1. Combining with Raman and LDA thus provides a general approach for studying the vibrational and structural properties of 2D layered materials with lower symmetry. ; Comment: accepted by Physical Review B; 23 pages, 3 figures, 4 tables