Humans have excellent predictive capabilities, and this anticipation would reflect in the interactions between people. In this work, we utilize the elliptical specification of the social force model (SFM) for pedestrian movements to study how anticipation affects motion dynamics. An elliptical potential determines the interaction between pedestrians not in contact. Anticipation is introduced by shaping the ellipse according to the relative velocity. By adjusting the time to extrapolate, we can control the strength of anticipation. Simulations are conducted in four typical scenarios, i.e., circular motion, crowd gathering, escape through a bottleneck, and free wander. In each case, the qualitative observations from visual animations are followed by quantitative analyses involving different indicators. Simulation results demonstrate that anticipation plays an important role in pedestrian dynamics in several aspects. Briefly, it helps stabilize the movement by reducing perturbations, facilitates a more ordered crowd configuration, and promotes spontaneous collective motion. The findings may set avenues for further research in anticipation dynamics.