Continuum arms are more adaptable to their environments and inherently human-friendly compared to their rigid counterparts. Path planning of continuum arms is an active research area with many challenges. The hyper-redundancy of continuum arms, which renders them highly versatile, is their curse in path planning. This problem becomes even more challenging in dynamic environments in the presence of mobile obstacles. In this paper, we propose an anticipatory path planning approach for continuum arms in dynamic environments. Our approach is based on obstacle prediction coupled with temporal graphs to model the dynamic environment. We evaluate the proposed approach’s performance and compare it to prevailing path planning approaches for continuum arms in dynamic environments.