Numerical models of the human body require realistic mechanical properties of the muscles as input, but, generally, such data are available only for animals’ muscles. As a consequence, the aim of this study was to identify the hyper-elastic behavior of the human sternocleidomastoideus muscle in tension using different constitutive laws. Ten sternocleidomastoideus muscles were tested in vitro. The hyper-elastic behavior was modeled with an exponential law and a hyper-elastic constitutive law studied analytically. The latter was also studied with an inverse approach using a subject-specific, finite-element model of each muscle. The three approaches were compared statistically. From these laws and methods, the shear modulus μ (4 to 98 kPa) and the curvature parameter α (17 to 52) were identified. Both the analytical and finite-element approaches gave parameters of the same order of magnitude. The parameters of the exponential and hyper-elastic laws were linked thanks to simple linear equations. Our results evidence that the hyper-elastic tension behavior of human sternocleidomastoideus muscle can be described using a simple model (exponential) considering basic geometric features (initial length and cross-sectional area).