Black phosphorus exhibits a high degree of band anisotropy. However, we find that its in-plane static screening remains relatively isotropic for momenta relevant to elastic long-range scattering processes. On the other hand, the collective electronic excitations in the system exhibit a strong anisotropy. Band nonparabolicity, due to interband couplings, leads to a plasmon frequency which scales as nβ, where n is the carrier concentration, and β<1/2. Screening and charge distribution in the out-of-plane direction are also studied using a nonlinear Thomas-Fermi model.