This article presents a numerical study of the stability of a hydraulic excavator during performing lifting operations. A planar dynamic model is developed with six degrees of freedom, which considers the base body elastic connection with the terrain, the front digging manipulator links, and the presence of the freely suspended payload. Differential equations describing the excavator dynamic behavior are obtained by using the Lagrange formalism. Numerical experiments are carried out to study the excavator dynamic stability under different operating conditions during the motion along a vertical straight-line trajectory. It is shown that the arising inertial loads during the movement of the links along the vertical trajectory, combined with the payload swinging and the motion of the base body, decreases the excavator stability. It was found that the excavator stability during following vertical straight-line trajectory decreases considerably in the lower part of the vertical trajectory. If the stability coefficient is close to 1, the payload swinging can cause the separation of a support from the terrain; nevertheless, the excavator stability can be restored. A method for tire stiffness and damping coefficients estimation is presented. The validation of the dynamical model is performed by the use of a smallscale elastically mounted manipulator.