Ionic polymer-metal composite (IPMC) is a promising material for soft-robotic actuator and sensor applications. This material system offers large deformation response for low input voltage and has an aptitude for operation in hydrated environments. Researchers have been developing IPMC actuators and sensors for applications with examples of self-sensing actuators, artificial fish fins and biomimicry of other aquatic lifeforms, and in medical operations such as in guided catheter devices. IPMCs have been developed in a range of geometric configurations, with tube or cylindrical and flat-plate rectangular as the most common shapes. Several mathematical and physics-based models have been developed for describing the transduction effects of IPMCs. In this work, the underlying theories of electromechanical and mechanoelectrical transduction in IPMCs are discussed, and simulated results of frequency response and shear response are presented. A model backbone is utilized which is primarily based on ion-transport and charge dynamics within the polymer membrane. The electromechanical model, that is with an IPMC as an actuator, is caused when an electric field is applied across the membrane causing ionic migration and swelling in the polymer membrane, which is based on the Poisson-Nernst-Planck equations and solid mechanics models. The mechanoelectric model is similar in underlying physics; however, the primary mechanisms of transduction are of different significance, where anion concentrations are as important as cations. COMSOL Multiphysics is utilized for simulations. Example applications of the modeling framework are presented. The simulated results provide additional support for the underlying physics theories discussed.