Abstract: Numerous soft and continuum robotic manipulators have demonstrated their potential for compliant operation in highly unstructured environments or near people. Despite their recent popularity, modeling of their smooth bending deformation remains a challenge. For soft continuum manipulators, the widespread, constant curvature approach to modeling is inadequate for modeling some deformations that occur in practice, such as combined bending and twisting deformations. In this paper, for the first time, we extend the classical Cosserat rod approach to model a variable-length, pneumatic soft continuum arm. We model the deformation of a pneumatically driven soft continuum manipulator, and the model is then compared against experimental data collected from a three degree of freedom, pneumatically actuated, soft continuum manipulator. The model shows good agreement in capturing the overall behavior of the bending deformation. In addition, the model shows good numerical stability for simulating long duration computations.