Octopuses are an example of dexterous animals found in nature. Their arms are flexible, can vary in stiffness, grasp objects, apply high forces with respect to their relatively light weight, and bend in all directions. Robotic structures inspired by octopus arms have to undertake the challenges of a high number of degrees of freedom (DOF), coupled with highly flexible continuum structure. This paper presents a kinematic and dynamic model for underwater continuum robots inspired by Octopus vulgaris. Mass, damping, stiffness, and external forces such as gravity, buoyancy, and hydrodynamic forces are considered in the dynamic model. A continuum arm prototype was built utilizing longitudinal and radial actuators, and comparisons between the simulated and experimental results show good agreement.