Animals are excellent at traversing obstacles in complex terrain by transitioning between locomotor modes. Our recent studies demonstrated that a potential energy landscape approach help understand how animals and robots transition between modes (Othayoth, Thoms, Li, 2020, PNAS). In that study, obstacles were uniform; however, in the real world, obstacles often vary spatially. In addition, our previous energy landscape model was quasi-static and did not capture stochastic dynamics common in locomotion. Here, we take the next step in establishing the energy landscape approach to locomotor transitions. We developed a stochastic dynamics simulation by applying the Langevin equation on a simplistic 2-D model system, a self-propelled circular body traversing two adjacent horizontal elastic beam obstacles on a flat ground, with one beam stiffer than the other. Body-beam interaction was determined by calculating collisional dynamics between rigid bodies and the gradient of the system’s potential energy landscape which describes elastic forces during continuous contact. On the landscape, the resistance of the two beam obstacles resulted in a potential energy barrier on each side, and the body could be trapped in an attractive basin in front of them. We found that increasing random force and self-propulsive force increased the body’s probability to escape from the basin and overcome a barrier to traverse. In addition, with one beam stiffer than the other, the body had a higher probability to escape by moving along trajectories that overcame the lower barrier. Our simple model was a proof of concept that potential energy landscapes can help statistically predict the distribution of trajectories of a self-propelled body traversing obstacles, which will be useful for control and motion planning of robots to traverse complex terrain.