This study evaluates the energy efficiency of pressure shock damping in a hydraulic lifting and leveling (HLL) module of a mobile robotic bricklaying system (RBS). The HLL module includes a servohydraulic actuator (SHA) and a hydraulic shock damper (HSD). The proposed adjustable HSD consists of a hydraulic accumulator circuit (HAC) and proportional damping valve. The frequency characteristics of the impedance and damping efficiency indices were used to evaluate the effectiveness of HSD damping. The dynamic responses of the SHA with and without HSD were analyzed based on a nonlinear state-space model. To control the damping of the pressure shock in the SHA-HSD system, a linear quadratic Gaussian (LQG) controller that follows two measurement signals was implemented. The LQG controller was adapted to the specific dynamic requirements of the SHA-HSD control system and nature of the RBS shock loads. The effectiveness of the LQG controller was evaluated during RBS operation under laboratory conditions. The main purpose of this study was to dynamically stabilize a leveled robot base subjected to shock loading during automatic operation of the RBS.