A 3-web with singularities is an ordered collection of three one-dimensional distributions L1, L2, L3 on a 2-dimensional manifold M. The subset Σ ⊂ M where these distributions are not pairwise transversal is called the singularity set. Under some conditions on Σ we find the differential invariants of the 3-web with singularities at the points of Σ and give examples of calculation of these invariants. © 2016, Pleiades Publishing, Ltd.