IR spectroscopy of CO adsorption (IR/CO) and Density Functional Theory (DFT) calculations on sulfide W/Al2O3 catalyst were investigated for an insight into the sulfide edge sites. Parallel between experimental and theoretical results allow to assign the ν(CO) bands at 2121 and 2066 cm-1 to CO adsorption on M- and S-edge sites of WS2 phase, respectively. Through a careful analysis of CO spectra on well-selected W catalysts, the molar attenuation coefficients for CO adsorbed on the two exposed edges could be determined. This allowed the morphology of WS2 slabs to be calculated. This work shows that increasing the W loading (6-20 wt% W) changes the slab morphology from an almost pure triangle exhibiting mostly M-edge to a truncated triangle. On W as well as on Mo sulfide catalysts, IR spectroscopy and DFT calculation show that CO adsorption allows to account for M- and S-edge sites, and thus of the morphology of sulfide slabs. It was shown that increasing the W loading shifts the slab morphology from a triangle exposing predominantly M-edge towards a more hexagonal shape. For close to monolayer coverage of alumina, Mo and W sulfide slabs present similar shape i.e. truncated triangle. However, edge sites of WS2 slabs clearly exhibit greater stability under H2 atmosphere than Mo sulfided ones.