Indentation is a widely used method to probe the mechanical properties of glasses. However, interpreting glasses’ response to indentation can be challenging due to the complex nature of the stress field under the indenter tip and the lack of in situ characterization techniques. Here, we present a numerical model describing the indentation of an archetypical soda-lime silicate window glass by means of peridynamic simulations. We show that, although it does not capture shear flow and permanent densification, peridynamics exhibits a good agreement with experimental indentation data and offers a direct access to the stress field forming under the indenter tip.