This paper studies the nonlinear dynamics of a two-degree-of-freedom vibro-driven capsule system. The capsule is capable of rectilinear locomotion benefiting from the periodic motion of the driving pendulum and the sliding friction between the capsule and the environmental surface in contact. Primary attentions are devoted to the dynamic analysis of the motion and stick-slip effect of the capsule system. Following a modal decoupling procedure, a profile of periodic responses is obtained. Subsequently, this work emphasizes the influences of elasticity and viscosity on the dynamic responses in a mobile system, whose implicit qualitative properties are identified using bifurcation diagrams and Poincaré sections. A locomotion-performance index is proposed and evaluated to identify the optimal viscoelastic parameters. It is found that the dynamic behaviour of the capsule system is mainly periodic, and the desired forward motion of the capsule can be achieved through optimal selection of the elasticity and viscosity coefficients. In view of the stick-slip motion, the critical equilibrium and its dynamic behaviours, different regions of oscillations of the driving pendulum are identified, with the attention focusing on the critical region where linearities are absent and nonlinearities dominate the dynamic behaviour of the pendulum. The conditions for stick-slip motions to achieve a pure forward motion are investigated. The proposed approach can be adopted in designing and selecting of suitable operating parameters for vibro-driven or joint-actuated mechanical systems.