Polymers and elastomers find nowadays a wide use in the field of the design of mechanical components and in many industrial applications. Elastomers show complex mechanical behaviors, like hyperelasticity, inelastic phenomena, hysteresis in cyclic loading and Mullins effect. Furthermore, creep and relaxation phenomena, and also a complex elastic modulus are experimentally evident. All these issues are object of this dissertation, where a comparison of principal numerical models available in literature is given; moreover, models are generalized or modified to fit properly the experimental data of the investigated materials. Dedicated techniques and test rigs for multiaxial mechanical tests are described. The strain distributions of the specimens are evaluated with a full-field approach, using optical measurement techniques. Besides the standard procedures for inverse problems, also the application of the "Virtual Fields Method" for material characterization is given.