In the framework of deployable structures, we focus on the modeling of tape springs, i.e. rod-like elastic bodies with thin-walled cross-section which develop localized folds due to a flattening of the cross-section. A rod model with highly deformable cross-section and few kinematics parameters is derived from a complete shell model, for large displacements, large rotations and dynamics. The simplicity of the model is achieved by introducing an elastica kinematics to describe the changes in the cross-section shape. This model is able to handle the formation of localized folds which can move along the rod line, merge or split, allowing to simulate complex scenarios of folding and deployment.