Vulcanized rubbers are commonly used to provide the energy absorption under compressive deformation from other engineering components. However, if a constant compressive deformation is maintained on rubber, the load response is not constant but decreases with time; i.e., the stress relaxation. A decrease in force response with time of rubber can be experimentally evaluated by the stress relaxation test. In the present work, the localized stress of vulcanized rubber during a compressive stress relaxation test (i.e., ASTM D6147) was evaluated. Hyperelastic behavior was assumed during rapid application of strain, while the viscoelastic behavior was assumed during stress relaxation. Hyperelastic and viscoelastic parameters were experimentally evaluated using a standard specimen. Finite element analysis (FEA) models were applied for the predictions of stress relaxations of rubbers with various geometries and applied strains. FEA results were in good agreement with results of the stress relaxation tests. Localized stresses in rubber during rapid application of compressive strain and stress relaxation were successfully evaluated. The findings can give the localized phenomena of vulcanized rubber during a stress relaxation test, which can be used as a guideline for the design, usage, and improvement of rubber and viscoelastic polymeric components.