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The new and promising field of soft robotics has many open areas of research such as the development of an exhaustive theoretical and methodological approach to dynamic modeling. To help contribute to this area of research, this paper develops a dynamic model of a continuum soft robot arm driven by cables and based upon a rigorous geometrically exact approach. The model fully investigates both dynamic interaction with a dense medium and the coupled tendon condition. The model was experimentally validated with satisfactory results, using a soft robot arm working prototype inspired by the octopus arm and capable of multibending. Experimental validation was performed for the octopus most characteristic movements: bending, reaching, and fetching. The present model can be used in the design phase as a dynamic simulation platform and to design the control strategy of a continuum robot arm moving in a dense medium.