Elastomers are typically assumed to be incompressible in most modeling approaches. However, performing simple tension and bulk tests, we show that some class of elastomers can experience significant volume changes when large deformations are involved. Existing volumetric strain energy density (SED) functions found in literature struggle to accurately capture these large volumetric deformations. To address this limitation, we propose a novel volumetric SED capable of: (1) accurately representing the response of rubbers under both small and large volumetric deformations; (2) reproducing different behaviors in case of volume shrinkage and volume expansion; (3) being adaptable to other compressible materials like soft tissues, foams and gels. Building upon the deviatoric–volumetric split of the strain energy function, we integrate the Yeoh-Fleming hyperelastic model as the deviatoric part of our proposed SED. Through comprehensive parameter calibration against experimental data from simple tension and bulk tests, we validate the effectiveness of our combined SED in accurately modeling elastomer responses to both shape and volume deformations. This proposed SED holds promise for implementation in numerical simulations to tackle more intricate problems involving compressible materials.