The companion paper presents a new three-parameter model for the uniaxial rate-sensitive material response, which is based on a bilinear static stress-strain relationship with kinematic strain-hardening. This paper extends the proposed model to trilinear static stress-strain relationships for steel and concrete, and discusses the implementation of the new models within an incremental-iterative solution procedure. For steel, the three-parameter rate-function is employed with a trilinear static stress-strain relationship, which allows the utilisation of different levels of rate-sensitivity for the plastic plateau and strain-hardening ranges. For concrete, on the other hand, two trilinear stress-strain relationships are used for tension and compression, where rate-sensitivity is accounted for in the strain-softening range. Both models have been implemented within the nonlinear analysis program ADAPTIC, which is used herein to provide verification for the models, and to demonstrate their applicability to the rate-sensitive analysis of steel and reinforced concrete structures.