The investigation of structural single rocking walls (SRWs) continues to gain interest as they produce self-centering lateral load responses with reduced structural damage. The Simple Rocking Model (SRM) with modifications has been shown to capture these responses accurately if the SRW and its underlying base are infinitely rigid. This paper advances previous rocking models by accounting for: 1) the inelastic actions at or near the base of the SRW; and 2) the flexural responses within the wall. Included in the proposed advancements are hysteretic and inherent viscous damping associated with these two deformation components so that the total dynamic responses of SRWs can be captured with good accuracy. A system of nonlinear equations of motion is developed, in which the rocking base is discretized into fibers using a zero-length element to locate the associated compressive deformations and damage. The flexural deformations of the rocking body are captured using an elastic term, while the impact events are modeled using impulse-momentum equations. Comparisons with experiments of structural precast concrete and masonry SRWs show that the proposed approach accurately estimates the dynamic responses of different SRWs with and without unbonded posttensioning, for various dynamic excitations and degrees of hysteretic action. Using the proposed approach, a numerical investigation employs different configurations of structural SRWs to quantify the various sources of energy loss, including hysteretic action and impact damping, during various horizontal ground motions.