<p>Using discrete element modeling, the unique characteristics of a bed of grains contained in a translating rectangular box with or without acceleration on a straight horizontal path have been studied. The inclined free surface shape has apparent similarities to its hydrodynamic equivalent at constant acceleration; nevertheless, due to the particle nature of the medium, there are some distinct differences. One of the notable differences is the nonlinear free surface of the granular bed. The effective slope of the accelerating granular bed is much higher compared to that of the liquid pool for the same dynamic condition. In the accelerating granular bed, the free surface profile is not affected by the particle density, but the particle size and inter-particular friction weakly influence it. Meanwhile, acceleration has an impact on the local gradient of the free surface. Nonetheless, the simulation results clearly imply that although typically, bed behavior is similar to solid body motion, locally, the discrete nature of the medium influences the distribution and motion of the particles. Contrary to the hydrodynamics case, a translation without acceleration also results in a slope in the free surface of the granular bed.</p>