In developing organisms, internal cellular processes generate mechanical stresses at the tissue scale. The resulting deformations depend on the material properties of the tissue, which can exhibit long-ranged orientational order and topological defects. It remains a challenge to determine these properties on the time scales relevant for developmental processes. Here, we build on the physics of liquid crystals to determine material parameters of cell monolayers. Specifically, we use a hydrodynamic description to characterize the stationary states of compressible active polar fluids around defects. We illustrate our approach by analyzing monolayers of C2C12 cells in small circular confinements, where they form a single topological defect with integer charge. We find that such monolayers exert compressive stresses at the defect centers, where localized cell differentiation and formation of three-dimensional shapes is observed.