The shape of human tongue plays an important role in oral cavity functions such as speaking, chewing, swallowing, and breathing. In this study, the authors constructed a mathematical model of the tongue using the mass-spring model and simulated tongue deformation during vowel production. The viscoelasticity of tongue tissues are represented by the Kelvin-Voigt model. Contraction of lingual muscles are represented by a muscle model composed of a constractile component, springs, a damper, and mass. Incompressibility of muscles is an important factor that affects tongue shape. In this study, the potential energy function generated by compression of tissues is defined. Muscle incompressibility is modeled by minimizing the energy function in the deformation process. The authors simulated tongue deformation during Japanese vowel production. Tongue muscles are classified into eight groups, and the muscle length is defined based on an MR image. The results are in good agreement with the MR imaging results of deformation of the tongue in the sagittal plane. Further, this simulation can qualitatively represent tongue deformation in producing Japanese vowel “a”.