Though brittle, silicate glasses undergo plastic deformation at the microscopic scale. Mechanical contact and indentation are the most common situations of interest. The plasticity of glasses is characterized not only by shear flow but also by a permanent densification process. After indentation, densification can locally reach 20\% in a pure silica glass. In this paper, a new constitutive model, derived from experimental observations is presented to account for the plasticity of fused silica. The use of nanoindentation tests to identify the plastic behavior of amorphous silica is discussed. A set of material properties is determined by comparing experimental load/displacement indentation curves to the results of finite element simulations. The numerical results show good agreement with recent experimental indentation-induced densification maps obtained by Perriot {\it et al.} [{\em J. Am. Ceram. Soc.}, 89:596--601, 2006].