This work presents a stiffness‐proportional viscous damping model based on the material component of the total tangent stiffness matrix. It is developed for nonlinear geometric inelastic frame analysis and implemented with distributed plasticity formulations. The use of a corotational approach allows isolating the nonlinear effects arising from material and geometric sources, hence allowing to preclude the contribution of the latter to simulate non‐modelled sources of energy dissipation. Following the presentation of the theoretical framework and a discussion on the physical meaningfulness of the proposed approach, several illustrative case studies are presented. The first is based on the damped free vibration response of a slender cantilever with elastic response, whereas the second addresses the seismic behavior of an inelastic reinforced concrete cantilever column. Comparisons with the total‐tangent‐stiffness‐proportional approach showcase the advantages of the current proposal.